This article reviews research on the unsupervised learning of morphology, that is, the induction of morphological knowledge with no prior knowledge of the language beyond the training texts. This is an area of considerable activity over the period from the mid 1990s to the present. It is of particular interest to linguists because it provides a good example of a domain in which complex structures must be induced by the language learner, and successes in this area have all relied on quantitative models that in various ways focus on model complexity and on goodness of fit to the data.