Valuations are finitely additive measures on convex compact sets. The theory of valuations is a classical part of convexity. Valuations continuous in the Hausdorff metric play a special role and we will concentrate in the talk on this class of valuations. In recent years there was a considerable progress in the theory and its applications. We will describe some of the progress with particular focus on the multiplicative structure on valuations and its applications to kinematic formulas of integral geometry.