The technique of Tashkinov trees is an important tool that has been used to obtain many significant results on edge colouring of multigraphs. We describe the method and its main motivation, the famous Goldberg-Seymour conjecture from the 1970's. We also outline several results from the last decade that have used the Tashkinov trees technique.

This talk is intended as an introduction, overview and survey to accompany the upcoming short course "Edge colouring of multigraphs and the Tashkinov trees method" (Oct 26-29).