Traditionally, motion estimation and segmentation have been performed mostly in the spatial domain, i.e., using the luminance information in the video sequence. Frequency domain representation offers an alternative, rich source of motion information, which has been used to a very limited extent in the past, and on relatively simple problems such as image registration. We review our work during the last few years on an approach to video motion analysis that combines spatial and Fourier domain information. We review our methods for (1) basic (translation and rotation) motion estimation and segmentation, for multiple moving objects, with constant as well as time varying velocities; and (2) more complicated motions, such as periodic motion, and periodic motion superposed on translation. The joint space analysis leads to more compact and computationally efficient solutions than existing techniques.