Why do people enjoy jigsaw puzzles, which--challenging and time-consuming as they are--might be considered more like work than play? The author investigates the motivations, preferences, and satisfactions of individuals working on jigsaw puzzles, and she explores how these elements of play relate to the procedures and strategies puzzlers use to assemble their jigsaws. She identifies four general approaches to completing these puzzles: the Explorer, Detective, Matchmaker, and Lion Tamer. She then describes how those who use these approaches differ in their openness to serendipity and flexibility, their attraction to the aesthetics of the puzzle picture, the degree of difficulty they embrace, and their relative interest in the process of puzzle assembly or in producing a finished puzzle. She concludes that the study of jigsaw puzzling helps us better understand leisure activities in general by allowing us more effectively to distinguish serious from casual leisure, explore the relationship of work to play, assess the importance of rules, investigate the relationship between product and process in play, and identify some of the intrinsic rewards that motivate play.