The Rauzy induction is the combinatorial counterpart of the Teichmuller flow. Its study is central in the proof of many of the dynamical results in Teichmuller dynamics such as the exponential mixing property, existence and unicity of an invariant measure of maximal entropy, ... After giving an introduction to this induction in the case of abelian and quadratic differentials, I will explain a generalization to multidimensional continued fractions, as well as a ergodicity criterion, and construction of invariant measures.