Under some conditions, sediments are entrained as a mobile bed by a turbulent liquid flow. This kind of transport, known as bedload, is found when the shear forces can displace some grains without fluidizing the bed. In such cases, due to the flow field, the granular bed may be unstable, generating ripples and dunes. These bedforms are observed both in nature (on riverbeds, for example) and in industry (in oil pipelines conveying sand, for example). In both cases, the friction between the bed and the liquid is increased, being related to flooding (in open channels) and high pressure drops (in closed conduits). This chapter is devoted to the problem of instabilities of granular beds. It presents stability analyses for the initial bedforms, their nonlinear evolution, and the effects caused by the free surface. The theoretical approaches are presented and compared with experimental data, showing a complete picture for this problem. © 2013 Nova Science Publishers, Inc. 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