Memories are mental states with a number of interesting features. This chapter maps the different positions on this issue, and highlights the virtues and difficulties for each of the options. It specifies the question of what the intentional objects of memory are by clarifying the relevant notions of memory and intentional object. The chapter motivates the significance of identifying the intentional objects of memory by exploring the relations between, on the one hand, the intentionality of memory and, on the other hand, the phenomenology and the epistemology of memory. It considers two natural candidates for being the intentional objects of memory, namely, worldly entities and mental entities, and develops some concerns for each of the two candidates. A promising alternative will emerge, as preserving the virtues of the two original candidates while avoiding their difficulties. The chapter concludes by sketching how the alternative candidate can shed some light on the phenomenological and epistemological issues.