Visual object recognition is complicated by the fact that the same 3D object can give rise to a large variety of projected images that depend on the viewing conditions, such as viewing direction, distance, and illumination. This paper describes a computational approach that uses combinations of a small number of object views to deal with the effects of viewing direction. The first part of the paper is an overview of the approach based on previous work. It is then shown that, in agreement with psychophysical evidence, the view-combinations approach can use views of different class members rather than multiple views of a single object, to obtain class-based generalization. A number of extensions to the basic scheme are considered, including the use of non-linear combinations, using 3D versus 2D information, and the role of coarse classification on the way to precise identification. Finally, psychophysical and biological aspects of the view-combination approach are discussed. Compared with approaches that treat object recognition as a symbolic high-level activity, in the view-combination approach the emphasis is on processes that are simpler and pictorial in nature.