The central puzzle of persuasion is why a receiver would listen to a sender who they know is trying to change their beliefs or behavior. This article summarizes five approaches to solving this puzzle: (1) some messages are easier to send for those with favorable information ( costly signaling), (2) the sender and receiver have common interest, (3) the sender messages are verifiable information, (4) the sender cares about their reputation for competence/honesty, and (5) the sender can commit to a messaging strategy (often called ‘Bayesian Persuasion’). After reviewing these approaches with common notation, I discuss which provide insight into prominent empirical findings on campaigns, partisan media, and lobbying. While models focusing on commitment have rapidly become prominent (if not dominant) in the recent theoretical literature on persuasion in political science and economics, the insights they provide are primarily technical, and are not particularly well-suited to explaining most of these phenomena.