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All animals, including humans, search for a variety of different things in their natural environment, from food to mates to a suitable place to live. Most types of search can be represented as stopping problems of varying complexity, in which the animal has to decide when to stop searching and accept the current option. All forms of search take time, and in solving a stopping problem the animal has to trade off this time cost against the expected benefits of continuing to search. This chapter discusses two main approaches to predicting search behavior: the optimality approach and the heuristics approach. The optimality approach identifies the best possible solution to a search problem and thereby sets an upper bound to what natural selection can achieve. The heuristics approach considers simple decision algorithms, or “rules of thumb,” which animals may use to implement efficient search behavior. Although few studies have tried to integrate these functional and mechanistic perspectives, they are likely to provide complementary insights. Often, the form of an optimal strategy suggests which kinds of heuristics might be expected to evolve. Stopping problems may be simple, repeated, or embedded in other stopping problems. For example, if searchers assess the value of each encountered option by examining a series of cues, the assessment process can be considered as another stopping problem. When the searcher is uncertain about the environment it is in, its previous experiences during search can strongly influence the optimal behavior. Where a limited number of items can be accepted, as in mate search, a key constraint is whether the searcher can return to previously encountered items. Some search problems are complicated by the fact that the encountered items are themselves searching. The chapter concludes with a discussion of some open questions for future research.