Economic systems produce robust statistical patterns in key sate variables including prices and incomes. Statistical equilibrium methods explain the distributional properties of state variables as arising from specific institutional, environmental, and behavioral postulates. Two broad traditions have developed in political economy with the complementary aim of conceptualizing economic processes as irreducibly statistical phenomena but differ in their methodologies and interpretations of statistical explanation. These conceptual differences broadly mirror the methodological divisions in statistical mechanics, but also emerge in distinct ways when considered in the context of social sciences. This paper surveys the use of statistical equilibrium methods in analytical political economy and identifies the leading methodological and philosophical questions in this growing field of research.