Information-seeking is usually conceived of as gathering information to make better decisions by observing and sampling from the external world. But for humans and many other intelligent agents, much of that information, once gathered, is also stored to guide future decisions, necessitating mechanisms for seeking information in some form of inner space. Here we survey various types of evidence suggesting that strategies adapted for search in external spatial environments are also used to seek information internally from memory. These include foraging strategies such as area-restricted search, which adaptively balances exploitation of locally clustered resources with exploration for resources more widely dispersed. We also describe how internal search satisfies the predictions of external foraging theory via the Marginal Value Theorem and show how these predictions can be used to investigate individual differences in memory search such as those caused by aging and cognitive impairment. Finally, we consider evidence that the structure of inner space may be a result of the very processes we use to search it.