Possums can be cute and cuddly, but unlike dogs and cats, may not be suitable for domestication as pets. If your property is located in bushland, you might even find a possum inside your house, but keeping wild possums as pets is not recommended!
If you live in a suburb of a city of Australia, chances are that your neighborhood is home to a possum population. Possums have been able to adapt to the artificial nature of suburbia, and you might occasionally find a possum inside your house. If you do, its best not to keep it inside -- rather, you should let it out. If a wild possum finds its way into your house, keep in mind that, depending on your jurisdiction, you may be able to trap the possum, but will most likely not be able to keep it as a pet. For example, in the state of Victoria, keeping a wild possum as a pet is prohibited, although if you have a Private Wildlife License, you may be able to purchase captive-bred possums to keep as pets. In some states, trapping a Common Brushtail Possum living inside a building may be legal, although trapping a possum in your garden (or keeping any possums you may trap) might be illegal.
Wild possums are generally not suitable as pets, and in some instances, keeping them as such may be illegal. Before searching for a possum to keep as a pet, you should research not only the practicalities of doing so, but also the laws in your jurisdiction. You might find that possums are a protected species!