What types of marsupials live in Australia?

There is a range of Australian marsupials.

Herbivores include many (not all) species of kangaroos such as the Red and Grey kangaroos, tree kangaroos, wallabies, wallaroos, quokkas, koalas and wombats.
Carnivores (the dasyurids) include the quoll, Tasmanian devil, and the recently extinct Thylacine, also known as the Tasmanian tiger, as well as the smaller dasyurids such as the kowari, dibbler, antechinus, ningaui, dunnart, planigale and phascogale.
Omnivores include some of the gliders and possums (e.g. Mountain pygmy possum), the bilby and the bandicoots.
Insectivores include the numbat and the marsupial mice.

Among these groups, there are terrestrial marsupials which spend all of their time on the ground (wombats, quokkas, wallabies); and arboreal marsupials which spend most of their time in trees (koalas, possums and gliders).

No marsupials in Australia are semi-aquatic.