There are three families: two with just a single member, and one, Dasyuridae, with about 55 members.
Unlike herbivores, which tend to become highly specialised for particular ecological niches and diversify greatly in form, carnivores tend to be broadly similar to one another, certainly on the level of gross external form. Just as northern hemisphere carnivores like cats, foxes and weasels are much more alike in structure than than, for example, camels, goats, pigs and giraffes, so too are the marsupial predators constrained to retain general-purpose, look-alike forms—forms which mirror those of placental carnivores. The names given to them by early European settlers reflect this: the Thylacine was called the Tasmanian Tiger, quolls were called native cats, and so on.
The primary specialisation among marsupial predators is that of size: prior to the massive environmental changes that came about with the arrival of humans about 50,000 years ago, there were several very large carnivores, none of them members of the Dasyuromorphia and all of them now extinct. Those that survived into historical times ranged from the wolf-sized Thylacine to the tiny Long-tailed Planigale which at 4 to 6 grams is less than half the size of a mouse. Most, however, tend towards the lower end of the size scale, typically between about 15 or 20 grams and about 2 kilograms, or from the size of a domestic mouse to that of a small domestic cat.
To provide context, the table below also shows the other major branches of the Australidelphia (Australasian marsupial) tree.