The chromatic number of a tournament $T4 is the smallest number of transitive tournaments that partition $V(T)$. Let us say that a tournament $S$ is a hero if for every tournament $T$ not containing $S$, the chromatic number of $T$ is at most a constant $c(S)$. Recently, in joint work with Eli Berger, Krzysztof Choromanski, Jacob Fox, Martin Loebl, Alex Scott, Paul Seymour and Stephan Thomasse, we proved a theorem that gives a complete description of all heroes. This talk will describe the result, and survey some of the proof ideas.