The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference 'Representation Theory of Real Reductive Lie Groups' held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature. This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields.