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It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the extraordinary generation properties of simple groups, focussing on topics such as random generation, (a,b)-generation and spread, as well as highlighting the application of probabilistic methods in the proofs of many of the main results. We also present some recentarXiv:1710.10434v1 fatcat:l7knkpjf3ved3okyow5hjxp7mm