Antarctic territorial claims are important to understanding the history and future possibilities of the Antarctic region. Geopolitical tensions arising from states’ different attitudes to territorial sovereignty in Antarctica (commonly referred to as the ‘Antarctic problem’) marked the history leading up to the 1959 Antarctic Treaty. This chapter examines the contributions of Argentina and Australia to the development of specific legal norms and principles to regulate the acquisition of territories in Antarctica. While the Antarctic Treaty put debates about territorial claims on the continent on hold, these claims still play a role in shaping the legal and institutional regime of Antarctica.