i will talk about joint work with siegfried echterhoff and rufus willett in which we introduce and study amenable actions of locally compact groups on c*-algebras, building on previous similar notions by anantharaman-delaroche for actions of discrete groups. among the new results we prove an extension of matsumura's theorem giving a characterisation of the weak containment property (coincidence of full and reduced crossed products) for actions on commutative c*-algebras and give examples showing that this result does not extend to general noncommutative c*-algebras.