This chapter presents the results of a survey of the grammatical expression of possession in a balanced sample of thirty Australian languages. Pama-Nyungan languages exhibit a relatively unified pattern, typically featuring an adnominal construction where the dependent is marked; as well as another adnominal construction where neither the possessor nor the possessum are marked, but they share case marking. The latter construction normally specializes for inalienable possessions. Non-Pama-Nyungan languages present more diversity. Their adnominal possessive constructions, are more often head-marking but vary in their marking strategies. Few non-Pama-Nyungan languages have a second adnominal construction for inalienable possessions, however some have traces of it, and others have clausal inalienable constructions. Possessive constructions can delineate more than one class, and some Australian languages exhibit relatively complex yet understudied systems. Interestingly, the semantics of inalienable classes of nouns is remarkably coherent, across the Pama-Nyungan/non-Pama-Nyungan divide, and independently of the type of construction involved.