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This is the written version of the Bourbaki seminar given in January 2013 andpublished in 2014 (modulo an additional early reference added subsequently). Itdescribes the first construction of infinite, finitely generated amenablesimple groups. It starts with a general study of topological-full groups, alongwith indications on the first appearances of such groups. Then the theorem isproved, namely that the derived subgroup of the topological-full group of aninfinite minimal subshift is both simple and finitely generated (Matui 2006)and amenable (Juschenko-Monod 2013, after being conjectured byGrigorchuk-Medynets). Some other properties of these groups are discussed. Noneof the numerous subsequent developments since 2013 are mentioned.

Groupes pleins-topologiques [d'apr\`es Matui, Juschenko, Monod...]