Contains the proceedings of the AMS Special Session "Operator Algebras and Their Applications: A Tribute to Richard V. Kadison”, held in January 2015. Among the topics addressed are the Kadison-Kaplanksy conjecture, classification of $C^*$-algebras, connections between operator spaces and parabolic induction, spectral flow, $C^*$-algebra actions, von Neumann algebras, and applications to mathematical physics.