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Quasi-Monte-Carlo methods are well-known for solving dierent problems of numerical analysis such a s i n tegration, optimization, etc. The error estimates for global optimization depend on the dispersion of the point sequence with respect to balls. In general, the dispersion of a point set with respect to various classes of range spaces, like balls, squares, triangles, axis-parallel and arbitrary rectangles, spherical caps and slices, is the area of the largest empty range, and it is a measure for the distribution of the points. The main purpose of our paper is to give a survey about this topic, including some folklore results. Furthermore, we prove several properties of the dispersion, generalizing investigations of Niederreiter and others concerning balls. For several well-known uniformly distributed point sets we estimate the dispersion with respect to triangles, and we also compare them computationally. F or the dispersion with respect to spherical slices we mention an application to the polygonal approximation of curves in space.