A group action is called amenable if there exists an invariant mean on the space. I will talk about a stronger property, namely the extensive amenability of group actions. This property was introduced by Juschenko and Monod, they constructed the first examples of finitely generated infinite amenable simple groups. These groups arise as commutator subgroups of topological full groups of minimal Z-actions on the Cantor set. We will see how extensive amenability can be used to prove the amenability of certain topological full groups.