'The International Conference on Hyperbolic Problems: Theory, Numerics and Applications', 'HYP2008', was held at the University of Maryland from June 9-14, 2008. This was the twelfth meeting in the bi-annual international series of HYP conferences which originated in 1986 at Saint-Etienne, France, and over the last twenty years has become one of the highest quality and most successful conference series in Applied Mathematics. The articles in this two-part volume are written by leading researchers as well as promising young scientists and cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of 'hyperbolic PDEs'. This volume will bring readers to the forefront of research in this most active and important area in applied mathematics.