This paper reviews recent theoretical studies of sand waves which are rhythmic large-scale bedforms observed in the continental shelf far from the near-shore region. Emphasis is given to the investigations carried out in the framework of the EU research project HUMOR. First, the results of linear morphodynamic stability analyses are described, which allow to understand the initial behavior of the sand waves. Hence, indications on the physical processes controlling the appearance and development of sand waves are obtained along with quantitative predictions of the wavelength of sand waves and of their migration speed. Then, nonlinear models are described which are used to predict the equilibrium profile of sand waves and their interaction with human interventions like sand extraction or the construction of pipelines. Finally, we discuss an analytical model which describes how the sand wave instability behaves when it is triggered locally; this leads to the generation, growth and expansion of a so-called sand wave packet.