The Cnidarians are a major, basally-branching, clade within the Eumetazoans, with strong similarities among themselves as well as differences. They have two archetypal body forms, the polyp and the medusa, and most lineages show an "alternation of generations", with medusae reproducing sexually to produce eggs that develop into polyps, which in turn bud off a succession of immature medusae, a form of asexual "reproduction". One of the shared features among them are cnidocytes (also called cnidoblasts, or nematocytes), poisonous harpoon-like cells that are used to capture prey and in various types of conflict.
One of the differences among the various lineages involves these two body forms: the Anthozoa lack a medusa form at all (as do various groups among other lineages), while the cubozoans undergo something much more reminiscent of a tadpole's metamorphosis into a frog: much or most of the polyp's body mass is taken up into a single medusa. This does not in any way constitute "reproduction", and in an earlier post I've argued that we should not regard the creation of multiple clones with the same genome as "reproduction" either: "reproduction" (among Eukaryotes) should be limited to the creation of new individual genomes, while the creation of new organisms with the same genome should be regarded as a form of "growth" of the individual. (Thus equating the individual with the genome. One commenter suggested "proliferation", at least with regard to single-celled organisms.)
Figure 1: Polyp (From Wiki)
Figure 2: Medusae (drawings by Haeckel; From Wiki)
Now, most (or at least many) Cnidarians have a "larval" form that develops quickly from the fertilized egg, and swims around a bit until it finds a spot to anchor and metamorphose into a polyp. In my view, however, calling this form a "larva" represents a misuse of the term that has led to an implausible, or at least improbable, picture of the origin and early evolution of the Cnidarians, with unfortunate results for the more general pictures of metazoan origins, especially when it comes to their nervous systems. ...
The typical Cnidarian "larvae" is a small, biradial, planula, usually non-feeding (although in some species it does do some eating).
This in contrast to the classic larvae we normally think of: insects and (vertebrate) amphibians. In the older clades of insects, the newly hatched nymphs bear some resemblance to the adult, although lacking wings. During their successive molts they become more adult-like, until in their final molt (next to final among mayflies) they have wings and are ready to reproduce. (In mayflies the penultimate molt, called subimago or to fly fishermen a dun, has wings, but only the final molt reproduces.) Examples include dragonflies, grasshoppers, roaches/termites, and preying mantises.
One insect clade, the Holometabola, invented the worm-like larva, a juvenile body form specialized for very rapid growth through a large size range: as much as 100,000 times larger at the final molt than when hatched. This larva has a simplified body, depending on easily expanded coeloms for support, and capable of expanding quite far in each molt. It has little or no resemblance to the adult form, although in some beetles the head comes to resemble the adult during the final few molts.
While the frogs and salamanders don't generally achieve the level of size increase found in many insects, their tadpoles are also well adapted for great expansion, with the legs only developing at something close to the adult size. As with the Holometabolous insects, then, the primary advantage of the larva is the ability to grow very rapidly during a short period when food is over-abundant, while the more sophisticated body plans of insect nymphs and juvenile amniotes grow more slowly, because they require more time and energy to modify their structure during size increase. Another issue is that their body plans are more specialized with regard to size: the square-cube law puts limitations on how far a single body plan can expand before it becomes too heavy for its support structures. (For this reason, creatures that live in water don't face as many problems with very large size increases as land creatures.)
When we compare these classic larvae with the "larvae" of Cnidarians, there is an obvious difference: the latter don't do much if any size expansion. In fact, according to the logic of insects and amphibians, it is the polyp form that represents the closest thing to a larva possessed by Cnidarians. This is especially true for those lineages that bud off multiple clones in medusa form, although the metamorphosis of the cubozoans is so reminiscent of frogs that it certainly brings the parallel to mind.
Moreover, the Anthozoa, which lack a medusa form, might well be compared to the axolotl, which is capable of undergoing sexual reproduction in larval form under some circumstances (although it retains a land-living adult form, unlike the Anthozoa). This process, in which a larval form acquires the ability to reproduce and loses the adult form, is a form of neoteny, a process which has been overused, in my view, in models of early animal evolution. Nevertheless, this is a case where I think it applies, contra the prevailing view of Cnidarian origins.
This prevailing view is that the polyp form is the ancestral form of the Cnidarian, with the early-branching Anthozoa having separated from the rest before their lineage developed the medusa form. In contrast, I would model the ancestral Cnidarian as a medusa already possessing a polypoid larva, which, like insect and amphibian larvae has been secondarily simplified while evolving its specializations for rapid massive growth. Just as the larvae of insects don't really resemble their immediate ancestors, although they have some similarities to more ancient ancestors, and just as the tadpole (lacking e.g. limbs) doesn't really resemble the immediate ancestors of the first land tetrapods, the polyp form doesn't (IMO) really represent the ancestral form of the medusa, but rather is a very simplified form with a few similarities to an ancestral form.
Why should we find an entire clade of very basally-branching Eumetazoans descended from such a highly specialized form? My answer begins with the distinction between coelenterates and cnidarians. The term coelenterate means an animal that uses its stomach (enteric system) as a coelom: an internal vessel filled with liquid under pressure that can do duty as a skeleton. I have suggested in the past that a fully formed coelom, with a complete epithelial system and muscles capable of compressing it in appropriate directions, is a much more sophisticated type of skeleton than is usually modeled, and in this case I would suggest that the coelenterates evolved by first developing a sphincter to close their gut against pressure, then developing the muscles and nerve control necessary to use it as a skeleton. (The early bilaterians, in my model, lacked such sphincters, as do the modern acoels, and only after various lineages had developed pass-through guts did they develop sphincters to close them off.)
In my view, then, the lineage leading to the Cnidarians started by becoming coelenterates, and underwent one or more massive explosions of adaptive radiation, creating a very large and diverse clade. Most of these were biradial, as were the original ancestors of the Ctenophores and the bilaterians. Some developed radial symmetry with higher indices than two, one of these being the ancestors of the Cnidarians.
It is the cnidocytes that set this lineage off from all the other coelenterates, and with the development of vertebrates (and various invertebrate clades) with more compact body plans, and more complex nervous systems dependent on greater circulation, the Cnidarians underwent their own massive expansion due to their excellent adaptation to preying on them, producing the lineages that survive today, along perhaps with a few that joined all the other coelenterates in extinction when out-competed by vertebrates and highly evolved invertebrates such as the arthropods and cephalopods.
There are several reasons that I consider my model much more plausible than the prevailing view. First, as I mentioned, the polyp form fits almost perfectly into the "classic" definition of larvae, as possessed by the Holometabolous insects and amphibians. Indeed, if not for the classification of the planula as "the" larval form, I suspect the polyp would have been assigned this role a long time ago. (Of course, the Cnidarians could have been defined as using hypermetamorphosis.)
Another reason is that the cnidocytes are a highly sophisticated adaptation, shared among all lineages of cnidarian. In my view, their development is extremely unlikely to have occurred simultaneously with the coelenterate adaptations, and if they had evolved first, it seems likely that some descendants would still be around, although I realize that absence of evidence is not evidence of absence. There could have been reasons that all the non-coelenterate cnidarians died out, although the existence of the Ctenophores argues against it. (The Ctenophores do not have a pressurized gut, although they do have the probably ancestral hollow gut they share with coelenterates and acoels.)
If the coelenterates developed first, they almost certainly would have undergone an explosion of adaptive radiation, considering that the ancestral bilaterians probably had not yet developed very far. It's worth considering that if, as I believe, the earliest feature that did service as a skeleton was a somewhat elastic structure right under the epidermis, sharing the features of cartilage and muscle, the addition of a high-pressure coelom would have allowed a massive increase in size, without much loss of ability to change body shape through muscular action. By contrast, the ctenophores, which retain such a skeleton and lack a coelom, have little ability to change shape, except for their tentacles, and they swim by means of cilia.
These three reasons are sufficient, IMO, to make this model far superior to one in which the ancestral Cnidarian was a polyp with cnidocytes, which then developed the medusa form. This, in turn, has important implications for metazoan evolution in general. The medusa form is much more sophisticated, with its water canals constituting a fairly complex skeleton,  a full-fledged neuroendocrine system, and a nervous system adapted to working with the skeleton to control swimming.    Many refinements have been developed by individual lineages, however it's very plausible that the common ancestor had the rudiments of most of them.
In this regard, I want to discuss a recent paper, Control of swimming in the hydrozoan jellyfish Aequorea victoria: subumbrellar organization and local inhibition (by Richard A. Satterlie). Here we have a report of multiple nerve nets serving different functions, linked by both chemical synapses and gap junctions. Both muscle and epithelial cells participate in the distribution of action potentials. The overall systems of control in various cnidarians is quite complex and sophisticated:
As a final word on the swimming system of hydromedusae, the organization of the motor network of the inner nerve ring is influenced by parallel sensory networks of the inner and outer nerve rings ([refs]). Furthermore, fourteen distinct conducting systems have been described in Aglantha ([ref]). In Aequorea, multiple statocysts are found throughout the bell margin ([ref]), and righting responses to tilt involve asymmetrical swimming contractions of the subumbrella, possibly including the local inhibitory mechanisms discussed here. These observations suggest that parallel and point-source pathways provide excitatory or inhibitory input to the swim motor network in the inner nerve ring of hydromedusae, pointing to an integrative organization that forms what can be argued to be a true central nervous system in these radially symmetrical organisms. In these animals, the `primitive' condition of diffuse, non-directional nerve nets has been modified in some conducting systems into a series of compressed, function-specific nerve networks that interact in the complex neural structures of the inner and outer nerve rings. As an example of the richness of function of the hydromedusan nervous system, one has to look no further than the organization of Aglantha ([ref]) to be impressed with the neural complexity of this `simple' animal group.Note that these conclusions are based on the prevailing view that the cnidarians began as a "simple" creature with a "simple" nervous system. In my view, the distributed nervous system isn't "simple" at all, but a sophisticated adaption to the cnidarian lifestyle, especially in terms of intra-specific territorial conflict (see below). Thus, we can plausibly model the cnidarian ancestor as having a fully functional central nervous system of sorts.
In this model, once the stem lineage had perfected the cnidocyte, various lineages of Cnidarian diverged along several paths. The cubozoans retained the ancestral metamorphosis, while refining their ability to see and control their swimming in the medusa form. They have surprisingly complex nervous systems.  (They also have the most powerful poisons, in general.) The Anthozoa, and multiple lineages within other clades, have undergone neoteny and lost the medusa form, building on the polypoid ability for rapid and massive growth. Most of the lineages ended up with a multiplier for their larval form, in that they produce a large number of medusoid clones, allowing them to adapt to longer local seasons of over-abundance.
What we must consider is that the polyp, as a larva rather than a retained ancestral form, represents a reversion (in some respects) to a very ancient ancestor: quite likely the common ancestor of the ctenophores, cnidarians, and bilaterians, and not necessarily the latest one at that. This means we can't use it as a measure of the sophistication of even the earliest ancestor of the coelenterates, especially when it comes to the nervous system. The specializations sufficient to control a medusoid form may well have been present in the last common ancestor of the bilaterians and coelenterates, and some of them may have been present in the last common ancestor of the ctenophores, coelenterates, and bilaterians, as well.
In addition, we must consider one of the key features of the coelenterates, their distributed nerve nets. These have been used to justify the assumption that this sort of nervous system was present in the common ancestor, but in fact these distributed nets are most likely adaptations to intraspecific conflict using cnidocytes. The process of evolving these highly adapted structures was almost certainly accompanied by territorial conflicts between individuals, and as they became better adapted for capturing prey, they also provided an increasing selective advantage for nerve nets that could suffer massive temporary shutdowns under the influence of the toxins involved. This allows us to paint a completely different picture of the nervous systems of the earliest animals.
It might be argued that the ctenophores have a mostly distributed nervous system as well, but we should note that they, also, probably represent the result of adaptive radiation from a single ancestor adapted to preying on coelenterates. Most of them retain this adaptation. It seems most plausible to me that the ctenophores co-evolved with their prey, acquiring and refining the ability to withstand the poisonous cnidocytes as their prey acquired and refined the cnidocytes. While part of this adaptation involved immunity to poisons, another part involved a more distributed nerve net. Another adaptation is their simplified structure, which does not reflect their rather sophisticated gene expression patterns.
The bottom line, then, is that when we look more carefully at the definitions and use of the word "larva", we can see a completely different, and potentially much more sophisticated, picture of the last common ancestor of the surviving Eumetazoans.
Satterlie, R. (2008). Control of swimming in the hydrozoan jellyfish Aequorea victoria: subumbrellar organization and local inhibition Journal of Experimental Biology, 211 (21), 3467-3477 DOI: 10.1242/jeb.018952
Links: Some of these aren't called out in the text. Unfortunately, too many of the most interesting are behind paywalls, I've done what I could to include open access articles covering the important points.
1. The evolution of nervous system centralization
2. Cnidarians and the evolutionary origin of the nervous system
3. Anatomy and development of the nervous system of Nematostella vectensis, an anthozoan cnidarian paywall
4. The neuroendocrine system of invertebrates: a developmental and evolutionary perspective
5. Developmental expression of homeobox genes in the ctenophore Mnemiopsis leidyi
6. Bilateral symmetric organization of neural elements in the visual system of a coelenterate, Tripedalia cystophora (Cubozoa) paywall
7. Control of swimming in the hydrozoan jellyfish Aequorea victoria: subumbrellar organization and local inhibition
8. Rhopalia are integrated parts of the central nervous system in box jellyfish paywall
9. Central neural circuitry in the jellyfish Aglantha: a model 'simple nervous system'