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Contents
1. Introduction
2. The $G$-equivariant enveloping von Neumann algebra
3. Amenable actions
4. The quasi-central approximation property
5. The weak containment property and commutant amenability
6. Actions on $X\rtimes G$-algebras and type I $C^*$-algebras
7. Regularity properties
8. Some new developments and questions



