Amenable action on a space is a powerful tool to study non-amenable groups. Classically such actions were introduced and studied by Zimmer and Anantharaman-Deraloche around 40 years ago. In this talk, I would like to talk on the non-commutative analogue of amenable actions. Four years ago, such actions were discovered in my work (1). After that, there are nice developments on this subject Particularly the right definition and characterizations of amenable actions are now clear, thanks to many researchers, including my joint work with Ozawa (3). And it turned out that amenability of the action, rather than amenability of the group, is the essential ingredient for the classification theory of equivariant Kirchberg algebras (2). I also introduce a new (functorial) construction of amenable actions on simple C*-algebras (3). References: (1)Y. Suzuku, Simple equivariant C*-algebras whose full and reduced crossed products coincide. J. Noncommut. Geom. 13 (2019), 1577--1585 (2)Y. Suzuku, Equivariant O_2-absorption theorem for exact groups. Compos. Math. 157, Volume 7, 1492--1506 (3)N. Ozawa, Y. Suzuki, On characterizations of amenable C*-dynamical systems and new examples Selecta Math.(N.S.) 27 (2021), Article number 92, 29pp