A functional Z defined on a space of real-valued functions {\mathcal F} is called a valuation if \[ Z(f\vee g)+Z(f\wedge g)=Z(f) +Z(g)\] for all $f,g\in {\mathcal F}$ such that the pointwise maximum $f\vee g$ and the pointwise minimum $f\wedge g$ are in $ {\mathcal F}$. The important classical notion of valuations on convex bodies in $\mathbb R^n$ is a special case of the rather recent notion of valuations on function spaces. We present new results on valuations on spaces of convex functions on ${\mathbb R}^n$ and continuous functions on ${\mathbb S}^{n-1}$. In particular, we discuss classification results for measure-valued valuations.