Geopolitics as a field was originally intended as a theoretical modelling of the relationship between fixed geographical circumstances and political choice. Now, the field is largely dominated by critical studies. It is almost considered axiomatic to include geopolitics as a theme in descriptive and analytical studies of the Arctic in global, regional, national and local contexts. This essay aims to review the core tenets of geopolitical thought and trace the categories and distinctions between the classical and critical approaches as applied in Arctic scholarship. It draws on highlights from the Arctic policy texts of three states demonstrating how assumptions and political options in terms of Arctic geographies can be expressed in different geopolitical frameworks. It is argued that revisiting and reviewing the core categories of geopolitics and their application in Arctic affairs can contribute to a better-informed understanding of how developments in the Arctic may unfold, as well as provide insights into the different functionalities of geopolitics.