To date there is no systematic exploration of the concept of ‘political feasibility’. We believe that feasibility is a central issue for political philosophy, conceptually as well as practically, and that it has been given background status for far too long. Roughly, a state of affairs is feasible if it is one we could actually bring about. But there are many questions to ask about the conditions under which we are justified in thinking that we could bring about a political state of affairs. In this article we bring together several aspects of the concept of feasibility defended in the literature thus far, and build upon them to give an analysis of the notion of political feasibility. We suggest that the notion involves a relation between agents and the pursuit of certain actions and outcomes in certain historical contexts, and that there are two important roles for feasibility to play in political theory, corresponding to two feasibility ‘tests’: one categorical, the other comparative. We show how the tests operate in the assessment of three different levels of a normative political theory: core normative principles, their institutional implementation and the political reforms leading to them. Focusing on the third level, which has received the least attention in the literature, we proceed to explain how feasibility considerations interact with desirability and epistemic considerations in the articulation of normative political judgments.