We introduce the concept of continuous translation-invariant curvature measures on a real finite dimensional vector space. As this generalizes various important notions in valuation theory, some classical results translate to the theory of curvature measures. In particular, Curv admits a grading analogous to McMullen’s decomposition and Curv can be equipped with a Banach space topology. Last, we will discuss some explicit characterizations of certain special classes of curvature measures.