Amenability for groups is a notion that was first introduced by von Neumann in 1929 to provide a conceptual explanation for the Banach-Tarski paradox. The notion has since been exported to many different areas of mathematics and continues to hold a distinguished position in fields such as group theory, ergodic theory, and operator algebras. For von Neumann algebras the notion plays a fundamental role, with the classification of amenable von Neumann algebras by Connes and Haagerup being considered a touchstone of the area. In this talk, I will give a survey of amenability and von Neumann algebras, emphasizing my own contributions related to von Neumann algebras associated with lattices in Lie groups.