Memories are mental states with a number of interesting features. One of those features seems to be their having an intentional object. After all, we commonly say that memories are about things, and that a subject represents the world in a certain way by virtue of remembering something. It is unclear, however, what sorts of entities constitute the intentional objects of memory. In particular, it is not clear whether those are mind-independent entities in the world or whether they are mental entities of some kind. The purpose of this chapter is to map the different positions on this issue, and to highlight the virtues and difficulties for each of the options. In Section 2, I will specify the question of what the intentional objects of memory are by clarifying the relevant notions of memory and intentional object. In Section 3, I will motivate 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. In Section 4, I will consider two natural candidates for being the intentional objects of memory, namely, worldly entities and mental entities, and I will raise some concerns for each of the two candidates. A promising alternative will emerge, in Section 5, as preserving the virtues of the two original candidates while avoiding their difficulties. The alternative will concern a certain combination of worldly and mental entities; a combination that involves both causal and truth-making relations. I will conclude by sketching how the alternative candidate can shed some light on the phenomenological and epistemological issues raised in the third section.