Ornithischia

   The ornithischians are an amazingly diverse group of dinosaurs linked by their possession of, among other things: at least five sacrals (uncertain in most basal forms); pubis rotated backwards, with a prepubic process of varying development pointing forward; no gastralia; a palpebral bone in the orbit (prong of bone cutting across outside of eye socket to varying degrees); ossified tendons at least above the sacral region (lost for tail mobility in stegosaurians); no phalanges on digit V of the foot; a recession in the jaw margins for "cheeks;" and finally, and to my mind most importantly, possession of an extra bone at the beak-end of the lower jaw, called a predentary, which is where the name Predentata, sometimes used for this group, comes from.  Ornithischians were basally small, bipedal ?herbivores (it is suggested that some ornithischians, particularly those with heterodonty [differing teeth], and the basalmost forms, were omnivorous, including heterodontosaurids with their fangs and some marginocephalians; some of the basal ornithischians, including an unnamed tooth form, may have been carnivorous), who by the MJ had produced an astonishing variety of body plans, including the spiky quadrupedal stegosaurians, the heavy-set armored ankylosaurians, and the small, fast basal ornithopods known informally as hypsilophodonts.  By the end of the Cretaceous, more had arrived, like the bulky iguanodonts and their descendants, the hadrosaurids, the horned ceratopsians, and the bone-headed pachycephalosaurians.
    Although ornithischians derive from bipedal ancestors, almost all of them show at least some ability to walk on all fours.  Ornithischians were primarily low browsers.  Unlike the other main group of classic dinosaurian herbivores, the sauropodomorphs, ornithischians display a wide variety of bodily features that appear to have been used for display and recognition, like the vertebral fins and headgear of hadrosaurids and some iguanodonts. 
    Large-scale ornithischian relationships have been stable and mostly unquestioned for the last 20 or so years, except for minor quibbles about where heterodontosaurids go, the position of Scelidosaurus vis-à-vis the ankylosaurians and stegosaurians, and if hypsilophodontids form a natural group.  There are some changes coming up, though, led by Richard Butler's work on basal ornithischians and new considerations on all of those tooth taxa from North America.  The main changes will affect the basal taxa and the hypsils.  This below is a version of the most current incarnation, which isn't too dissimilar to what came before except for Lesothosaurus and the heterodontosaurids.  Using Cerapoda and Ornithopoda may get harder, though.

<--Ornithischia
      |--Pisanosaurus       
      |--Heterodontosauridae
      |    |--Abrictosaurus
      |    `--Heterodontosaurinae
      |         |--Heterodontosaurus
      |         `--Lycorhinus 
      `--+--Eocursor
           `--Genasauria
                |--Thyreophora
                |    |--Scutellosaurus
                |    `--+--Emausaurus
                |         `--+--Scelidosaurus
                |              `--Eurypoda
                |                   |-->Ankylosauria
                |                   `-->Stegosauria
                `--Neornithischia          
                     |--Lesothosaurus
                     `--+--Stormbergia
                          `--+--Agilisaurus
                               `--+--Hexinlusaurus
                                    `--+--Othnielosaurus
                                         `--Cerapoda
                                              |-->Ornithopoda
                                              `--Marginocephalia
                                                   |-->Pachycephalosauria
                                                   `-->Ceratopsia  

Ornithischia to Genasauria:  Unlike theropods and sauropodomorphs, there is little good material for basal ornithischians.  Most of what was thought to be known for them were distinctive teeth, but after the Revueltosaurus affair these may not even be dinosaurian (check here to find if your favorite tooth taxon has been banished).

Ornithischia to Genasauria i.s.: Years ago, when all ornithischians were thought to have sprung from some sort of ornithopod or another, most of these animals would have been known as the most basal ornithopods, the "fabrosaurids."  Something like these animals is known from the Late Triassic Lower Elliot Formation of South Africa.  

Heterodontosauridae:  Heterodontosaurids are known mostly from skull material, with distinctive tusks found in most individuals.  They have been wild-cards, given the paucity of other early ornithischians to compare them to, and have been put with the ornithopods, or closer to the marginocephalians due to their jugal (cheek-area) bosses and tusks, the latter of which are also known in pachycephalosaurians, and some pelvic and hand details.  The most recent hypothesis is that they are a very basal offshoot of Ornithischia, which I'm using here.  This is still a hot issue, or at least it would be if ornithischians were charismatic predators.  Heterodontosaurid material may also be known from the Sinemurian-Pliensbachian (EJ) of the southwest U.S., the Norian (LTr) of Argentina, and the LTr of Europe.

Heterodontosauridae i.s.:

Heterodontosaurinae:

Genasauria i.s.:

Thyreophora: Thyreophora was revived in the 1980s to contain the armored dinosaurs, which by the early 1990s consisted of the ankylosaurians and stegosaurians.  There are few characters which support this clade, but one, the possession of keeled, dorsal, parasagittal armor, running head to tail, is pretty strong.  However, some researchers believe that the stegosaurians may not belong, which would leave the ankylosaurians alone here with some basal taxa.  More basal thyreophoran material may be known from the EJ of China.

Thyreophora i.s.:

Eurypoda i.s.

Neornithischia: Here again we see a spray of "fabrosaurs," this time grading into hypsil-type animals.  Agilisaurus and Hexinlusaurus appear to have lacked ossified tendons on the tail, an absence which would have made their tails much more flexible than most other ornithischians.
   "Othnieliidae" was never much more than a "vanity project" for Othnielia (now Othnielosaurus).  There may be a new, undescribed Spanish "othnieliid".  

Neornithischia i.s.: This grouping is for taxa that appear to fit somewhere in the vicinity of Othnielosaurus, basal Cerapoda, and the hypsilophodonts.

Cerapoda i.s.:  Cerapoda comes from Ceratopsia+Ornithopoda, and, as the name suggests, contains both, plus the pachycephalosaurians.  The name is rather unfortunate, in that mispronunciation can cause confusion with Sauropoda, which is composed of quite different dinosaurs. 

Marginocephalia i.s.: The marginocephalian families, Pachycephalosauria and Ceratopsia, are linked by several characters, including the bony shelf found at the back of the skull, which gives this group its name and forms a distinctive frill in ceratopsians.