For the classical motion invariant valuations on convex bodies, the intrinsic volumes, local variants exist, namely measure-valued additive and motion covariant functionals. These are the curvature measures. In view of applications in integral geometry, we study translation invariant functionals on convex bodies or convex polytopes which admit such a local version. We clarify the connection between these local functionals and valuations and also discuss whether valuations on convex polytopes which have certain continuouity properties allow an extension to all convex bodies.