The Euler characteristic of a non-empty (solid) polytope $P$ is the alternating sum of the number of non-empty $i$-dimensional faces of $P$. The Euler-Poincaré formula asserts that this alternating sum is equal to $1$. In this talk we discuss how the Euler characteristic can be constructed as a valuation. The construction has nice applications: we will see that it gives us simple proofs of the Euler-Poincaré formula and of a theorem on the number of regions in a hyperplane arrangement.