In 1952, Hugo Hadwiger established a remarkable classification result. He proved that all rigid motion-invariant, continuous valuations on the space of convex bodies (compact convex sets) in $\R^n$ are linear combinations of intrinsic volumes. Here, a functional Z defined on convex bodies is called a valuation (or additive) if \[\oZ(K)+\oZ(L)=\oZ(K\cup L) + \oZ(K\cap L) \] for all convex bodies $K$ and $L$ such that $K\cup L$ is again a convex body. In $\R^3$, the Hadwiger theorem states that for every rigid motion-invariant, continuous valuation $\oZ$, there are $c_0, c_1, c_2, c_3\in \R$ such that \[\oZ(K) = c_0 V_0(K) + c_1 V_1(K) + c_2 V_2(K) + c_3 V_3(K)\] for every convex body in $\R^3$. Here, $V_0(K)=1$ (the Euler characteristic) and $V_3(K)$ is the 3-dimensional volume of K, while $V_2(K)$ is (up to a constant multiple) the perimeter of $K$ and $V_1(K)$ its mean width. We will discuss this result, some of its consequences and applications, and some of the many results it inspired. In particular, we will describe a recent functional version of the Hadwiger theorem (joint work with Andrea Colesanti and Fabian Mussnig).