In this paper we survey most of the recent and often surprising results on packings of congruent spheres in d-dimensional spaces of constant curvature. The topics discussed are as follows: - Hadwiger numbers of convex bodies and kissing numbers of spheres; - touching numbers of convex bodies; - Newton numbers of convex bodies; - one-sided Hadwiger and kissing numbers; - contact graphs of finite packings and the combinatorial Kepler problem; - isoperimetric problems for Voronoi cells, the strong dodecahedral conjecture and the truncated octahedral conjecture; - the strong Kepler conjecture; - bounds on the density of sphere packings in higher dimensions; - solidity and uniform stability. Each topic is discussed in details along with some of the "most wanted" research problems.
['Károly Bezdek']
Sphere packings revisited