A k-dicolouring of a digraph is a partition of its vertex setinto k acyclic subdigraphs. The dichromatic number of a digraph D is the minimum k such that D has a k-dicolouring.

We first give some properties related to the dichromatic number in order to show why and how it generalizes the chromatic number of non-oriented graphs. Then we investigate the following questions: What can we say about subgraphs, induced subgraphs and topological minors of a digraph with large dichromatic number?