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In a recent paper , it is shown that the restrictions of bent functions to subspaces of codimension 1 and 2 are highly nonlinear. Here, we present an extensive study of the restrictions of bent functions to affine subspaces. We propose several methods which are mainly based on properties of the derivatives and of the dual of a given bent function. We solve an open problem due to Hou . We especially describe the connection, for a bent function, between the Fourier spectra of itsdoi:10.1109/tit.2003.814476 fatcat:kndedgfadvejhdwarzof46hjlm