Theropoda

    The theropods are somewhat bland on the surface, because they all followed a body plan devoted to bipedal hunting on the ground, but they had a healthy variety of styles and variations on their main theme.  It is fairly well settled that birds are closely related to theropods, although the placement and groups closest are not clear.  I used to follow a theory that claims flight was achieved by animals just before the first true dromaeosaurids, making a number of classic (historically considered non-avian and not having ancestors that could fly) theropods secondarily flightless, meaning they had ancestors that could fly, but they themselves had lost that ability.  This is between two other theories, known colloquially as BADD (Birds Are Dinosaur Descendants, with the emphasis here that no classic theropod was secondarily flightless) and BCF (Birds Came First, with the premise that all classic theropods were secondarily flightless).  Since I've gotten my copy of The Dinosauria II, I've finally come around to BADD.  
    The theropods were all bipedal, as far as is known, and the majority of the classic theropods were predators, with some exceptions: the oviraptorosaurians, troodontids, and ornithomimosauroids may have been herbivorous or omnivorous.  They all likely could move reasonably fast; the large theropods had their speed helped by their long legs.  By taking large strides quickly, they could move fast without running if they chose.  It is likely that at least all theropods that were members of Coelurosauria either were covered with a downy "protofeather" coating or had lost that characteristic. 
    Some important anatomical characters linking all theropods ancestrally include an extra hole in the skull's maxilla, a reduction or loss of both the fourth and fifth digit of the hand, hollow long bones, reduction of the fifth digit of the foot to almost nothing, and presacrals bearing holes (pleurocoels) to hollow centra.
    In the past, a group called the teratosaurids was considered to be the earliest "carnosaurs," and sometimes was aligned with the prosauropods.  This group was eventually discovered to be based on "thecodont" remains, sometimes mixed with prosauropods remains for good measure, but not before working its way into the popular literature.  A fair number of older (pre~1985) books on dinosaurs include (very hypothetical) restorations of "teratosaurids". 
    Although it was recently thought that a sauropod, Eobrontosaurus, had "belly ribs," it appears that only theropods and prosauropods had these, which would have protected the belly area.  In addition, many theropods have been restored with their palms facing down or back, which would have been impossible due to lack of the proper forearm rotation for most (if not all) of them.  Instead, theropod hands would have faced each other.
    An interesting possibility suggests that the adults of small theropods may have had to compete with the juveniles of large theropods, particularly if the parents had left the young to fend for themselves at an early age.  This in effect would have made these juveniles almost a separate species.  Theropods may have also done communal nesting, as suggested by remains found in Portugal.   
    An unusual small tooth from the Late Campanian of Mexico has a peculiar groove that could indicate the existence of a small, venomous theropod.

<--Theropoda
      |--?Guaibasaurus
      `-->Neotheropoda

Theropoda:

Theropoda i.s.:  Don't weep for most of these folks.  Aside from a couple of animals that appear to belong around this level, these creatures earned their status, being based on little material, often poor in quality.  More than a few tooth taxa appear in this following table, providing mute testimony to the fact that dinosaurs named from isolated teeth more often than not quickly enter into a usually richly-deserved obscurity.  Occasionally, one will rise from the depths like Troodon on the basis of uniqueness, but this is rare (in the old days of dinosaur paleo, a dubious tooth name like Trachodon could became host to a taxonomical monstrosity of names and material, very little of which could ever be shown to pertain to the host taxon).

Neotheropoda: This is getting into the more derived theropods, and starts off with a split between the coelophysoids and the other theropods, followed closely by the splitting-off of Ceratosauria.