Summary: The paper is concerned with statistical aspects of multivariate extreme value distributions. The family is infinite dimensional, so direct parametric estimation is not possible. We describe such nonparametric and parametric approaches, the latter being based on parametric subfamilies. Some problems connected with maximum likelihood estimators are discussed, and solutions proposed. In the nonparametric cases, the main method is an adaptation of the kernel method for density estimation. The detailed discussion is restricted to the bivariate case, but we also outline how the methods might be extended to higher dimensions.