The coat is thick, woolly, and soft. The tail is well furred, prehensile, and naked on the lower side for at least the terminal portion. Females of the genus have a well-developed pouch that opens forward and encloses two mammae. This brown-pigmented, sternal patch is more prominent in the male than in the female. Copious amounts of an anal gland secretion with a strong musky odor are also produced and may have a function in demarcating territory, as well as being a defense mechanism.
All species are nocturnal and arboreal and usually nest in tree hollows.
They generally occupy forest habitat, but T. vulpecula also may be found in areas devoid of trees, where it shelters by day in caves or burrows of other animals. It is even found in semideserts of central Australia, where it takes shelter in eucalyptus trees along watercourses. Resident populations occur in most cities in parks and suburban gardens, where the animals shelter on the roofs of houses. The diet consists mostly of young shoots, leaves, flowers, fruits, and seeds. Insects also are eaten, and there are well-documented records of T. vulpecula killing young birds.