The study of asymptotically locally Euclidean Kahler manifolds had a tremendous development in the last few years. This talk presents a survey of the main results and the open problems in this area. When the manifolds support an ALE Ricci flat Kahler metric the complex surfaces and their metric structures are well understood. The remaining case to be studied is that of ALE scalar flat Kahler manifolds. In this direction, the underlying complex manifold is described. It is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exists only finitely many diffeomorphism types of minimal ALE Kahler surfaces.