We describe the construction of the tame site associated with a morphism of schemes $X \to S$. It is a modification of the étale site of $X$. Its cohomology with coefficients prime to the characteristic coincides with étale cohomology and is better behaved for $p$-torsion coefficients in characteristic $p$. In contrast to the étale cohomology in positive characteristic, the tame cohomology is of a motivic nature. For instance, it is homotopy invariant. We will also discuss a possible connection with Suslin cohomology.