Bayesian methods and Bayesian inference are now ubiquitous in the social sciences, including political science and international relations. The reasons for this are numerous and include: a superior way to describe uncertainty, freedom from the deeply flawed Null Hypothesis Significance Testing paradigm, the ability to include previous information, more direct description of model features, and most recently statistical computing tools that make model computations easy. Yet this is not a static area in social science methodology, and new methodological developments are published at a rapid pace. The objective of this handbook chapter is to describe basic Bayesian methods, chronicle the recent history of their application in political science and international relations, and then highlight important recent developments.