In this chapter we consider unsupervised learning from two perspectives. First, we briefly look at its advantages and disadvantages as an engineering technique applied to large corpora in natural language processing. While supervised learning generally achieves greater accuracy with less data, unsupervised learning offers significant savings in the intensive labour required for annotating text. Second, we discuss the possible relevance of unsupervised learning to debates on the cognitive basis of human language acquisition. In this context we explore the implications of recent work on grammar induction for poverty of stimulus arguments that purport to motivate a strong bias model of language learning, commonly formulated as a theory of Universal Grammar (UG). We examine the second issue both as a problem in computational learning theory, and with reference to empirical work on unsupervised Machine Learning (ML) of syntactic structure. We compare two models of learning theory and the place of unsupervised learning within each of them. Looking at recent work on part of speech tagging and the recognition of syntactic structure, we see how far unsupervised ML methods have come in acquiring different kinds of grammatical knowledge from raw text.