Episodic memory refers to memory for specific episodes from one’s life, such as working in the garden yesterday afternoon while enjoying the warm sun and chirping birds. In the laboratory, the study of episodic memory has been dominated by two tasks: single item recognition and recall. In single item recognition, participants are simply presented a cue and asked if they remember it appearing during the event in question (e.g., a specific flower from the garden) and in free recall they are asked to generate all aspects of the event. Models of episodic memory have focused on describing detailed patterns of performance in these and other laboratory tasks believed to be sensitive to episodic memory. This chapter reviews models with a focus on models of recognition with a specific emphasis on REM (Shiffrin & Steyvers, 1997) and models of recall with a focus on TCM (Howard & Kahana, 2002). We conclude that the current state of affairs, with no unified model of multiple memory tasks, is unsatisfactory and offer suggestions for addressing this gap.