A digraph F is n-unadoidable} (resp. n-universal) if it is contained in every tournament of order n (resp. n-chromatic digraph). Well-known theorems imply that there is an n_F such that F is n_F-unavoidable (resp. n_F-universal) if and only if F is acyclic, (resp. an oriented forest). However, determining the smallest n_F for which it occurs is a challenging question. In this talk, we survey the results on unavoidability and universality and detail some recent recults obtained with various co-authors.