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In this survey paper, we characterize the learning problem in cognitive radios (CRs) and state the importance of artificial intelligence in achieving real cognitive communications systems. We review various learning problems that have been studied in the context of CRs classifying them under two main categories: Decision-making and feature classification. Decision-making is responsible for determining policies and decision rules for CRs while feature classification permits identifying and classifying different observation models. The learning algorithms encountered are categorized as either supervised or unsupervised algorithms. We describe in detail several challenging learning issues that arise in cognitive radio networks (CRNs), in particular in non-Markovian environments and decentralized networks, and present possible solution methods to address them. We discuss similarities and differences among the presented algorithms and identify the conditions under which each of the techniques may be applied.