The paper deals with the structure-motion problem for uncalibrated cameras, in the case that subsidiary information is available, consisting e.g. in known coplanarities or parallelities among points in the scene, or known positions of some focal points (hand-eye calibration). Despite unknown camera calibrations, it is shown that in many instances the subsidiary information makes affine or even Euclidean reconstruction possible. A parametrization by affine shape and depth is used, providing a simple framework for the incorporation of apriori knowledge, and enabling the development of iterative, rapidly converging algorithms. Any number of points in any number of images are used in a uniform way, with equal priority, and independently of coordinate representations. Moreover, occlusions are allowed.