Valuations form a well-understood class of maps in convex geometry. In more recent years, various examples of local versions of valuations have been studied. We will give a (preliminary) definition of "curvature measures" which attempts to unify these examples in a sensible manner. After translating some results from the theory of valuations to the theory of curvature measures, we conclude by classifying all curvature measures on the real line which already reveals the first differences between the theory of valuations and the theory of curvature measures.