Visibility computation was crucial for computer graphics from its very beginning. The first visibility algorithms in computer graphics aimed to determine visible surfaces in a synthesized image of a three-dimensional scene. Nowadays there are many different visibility algorithms for various visibility problems. We propose a new taxonomy of visibility problems that is based on a classification according to the problem domain. We provide a broad overview of visibility problems and algorithms in computer graphics grouped by the proposed taxonomy. We survey visible surface algorithms, visibility culling algorithms, visibility algorithms for shadow computation, global illumination, point-based and image-based rendering, and global visibility computations. Finally, we discuss common concepts of visibility algorithm design and several criteria for the classification of visibility algorithms.