People retrieve episodic memories about specific earlier events that happened to them. Accordingly, researchers have sought to evaluate the hypothesis that nonhumans retrieve episodic memories. The central hypothesis of an animal model of episodic memory is that, at the moment of a memory assessment, the animal retrieves a memory of a specific earlier event. We tested this hypothesis by ruling out non-episodic memory hypotheses. We developed a range of approaches, so that we have working models to evaluate elements of episodic memory in animals. These approaches include: what-where-when memory (Zhou & Crystal 2009, PNAS); source memory (Crystal, Alford, Zhou, & Hohmann 2013, Current Biology); binding of episodic memories (Crystal & Smith 2014, Current Biology); multiple item-in-context memories (Panoz-Brown et al., 2016, Current Biology); replay of episodic memories (Panoz-Brown et al., 2018, Current Biology); and answering unexpected questions after incidental encoding (Zhou, Hohmann, & Crystal 2012, Current Biology). In each approach, evidence for episodic memory comes from studies in which judgments of familiarity cannot produce accurate choices in memory assessments. These approaches may be used to explore the evolution of memory.