High-order behaviour and summation methods in perturbative QCD

After reviewing basic facts about large-order behaviour of perturbation expansions in various fields of physics, I consider several alternatives to the Borel summation method and discuss their relevance to different physical situations. Then I convey news about the singularities in the Borel plane, and discuss the topical subject of the resummation of renormalon chains and its application in various QCD processes.