The segmentation and word discovery problem arises because speech does not contain any reliable acoustic analog of the blank spaces between words of printed English. As a result, children must segment the utterances they hear in order to discover the sound patterns of individual words in their language. A number of computational models have been proposed to explain how children segment speech and discover words, including ten new models in the last five years. This paper reviews all proposed models and organizes them according to their fundamental segmentation strategies, their processing characteristics, and the ways in which they use memory. All proposed models are found to use one of three fundamental strategies: the utterance-boundary strategy, the predictability strategy, or the word-recognition strategy. Selected predictions of the models are explained, their performance in computer simulations is summarized, and behavioral evidence bearing on them is discussed. Finally, ideas about how these diverse models might be synthesized into one comprehensive model are offered.