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We provide a model of self-selection by candidates in a probabilistic voting environment to shed light on the forces shaping the quality of politicians from both the supply and demand sides of politics. The model highlights the idea that the patterns of selection and the comparative statics of politician quality depend critically on how the costs of running for office vary for candidates with different qualities. The model offers predictions on how the quality of the political class will vary with key parameters pertaining to both the supply and demand for candidates. We use the model to frame a review of the empirical literature on political selection that has emerged over the past two decades. We contrast areas where significant progress has been made with others where important theoretical predictions remain untested or existing evidence does not allow a consensus, highlighting areas for future research.