Erd\H{o}s and Arithmetic Progressions

This is a short survey article written for the Erd\H{o}s centennial conference in Budapest in 2013. The main two topics covered are Szemer'edi’s theorem and its ramifications, and the Erd\H{o}s discrepancy problem. There is an emphasis on what we do not yet know, so much of the article is somewhat speculative.