The study of Riemann problems has undergone a strong, steady growth in the last decade. The general direction of the research has headed toward understanding the wave structure of the solutions of more physically realistic systems. These systems fail either or both of the two main restrictions of the classical theory - that the system be strictly hyperbolic or genuinely nonlinear. The systems that have been studied tend to fall into the following broad classes: real gas dynamics (including combustion), visco-elastic materials, phase transitions, and multiphase flow in porous media. In addition to their usefulness in large-scale calculations, computational schemes have vastly improved the handling of discontinuity behavior.This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Current Progress in Hyperbolic Systems: Riemann Problems and Computations, held at Bowdoin College in July 1988. The papers presented here provide a complete picture of recent research by some of the leaders in this field. Graduate students and beginning researchers will find this book a useful introduction to current work in this area