I will present an overview of our research on gaze prediction and gaze guidance (see www.gazecom.eu). For prediction we use efficient visual representations (derived from differential geometry) to model visual saliency, and support-vector machines (SVNs) to obtain the predictions. An alternative approach to efficient representation is based on the principle of sparse coding. To obtain the local transformations needed for gaze guidance we use low-dimensional visual representations (signal energy on different spatio-temporal scales) and SVNs.