Understanding the vast array of phenomena exhibited by the many-body system of interacting electrons in matter is one of the great challenges of physics. It is now ~80 years since 1924 when Prince Louis de Broglie deposited his thesis. Within a few years quantum mechanics provided the underpinnings of present understanding of metals, insulators and semiconductors. Quantitative predictions for materials had to wait until ~40 years ago with the advent of density functional theory (DFT) in 1964 with the work of Kohn, Sham and Hohenberg. DFT provided a new approach to include effects of exchange and correlation among electrons into tractable independent-particle methods. Although DFT is formally exact, its usefulness depends upon the ability to make practical approximations. New algorithms and computational methods, notably the Car-Parrinello method published 20 years ago, have brought the field to the point where many properties of large classes of materials can now be determined directly from the fundamental equations for the electrons. The methods have become standard tools - an essential part of modern materials research. So what is new and challenging? The most interesting problems are strongly-correlated systems where present approximations for density functionals often fail. The challenge is to create new approaches that make possible robust predictions for new phenomena and materials, biological systems, nanostructures, metal-insulator transitions, superconductivity and many other areas. Specific examples of recent work show the power of combined independent-particle and many-body methods to provide new predictive capabilities and new insights into important problems in physics, chemistry, and materials science.