Assemblage thinking and actor-network theory (ANT) have been at the forefront of a paradigm shift that sees space and agency as the result of associating humans and non-humans to form precarious wholes. This shift offers ways of rethinking the relations between power, politics and space from a more processual, socio-material perspective. After sketching and comparing the concepts of the assemblage and the actor-network, this paper reviews the current scholarship in human geography which clusters around the four themes of deterritorialisation/reterritorialisation; power; materials, objects and technologies; and topological space. Looking towards the future, it suggests that assemblage thinking and ANT would benefit from exploring links with other social theories, arguing for a more sustained engagement with issues of language and power, and affect and the body.