New types of computer simulation are being used to investigate matter on the atomic scale. Unlike older simulation methods, the new techniques represent a solid or a liquid as a collection of nuclei and electrons, and the laws of quantum mechanics are used to calculate the energy and the forces from first principles. The most successful method so far for doing first-principles simulation is based on density functional theory and the pseudopotential approximation. I describe the main ideas of these techniques and explain how they can be used to perform simulations in which chemical bonds are made and broken. I give illustrations of current work in two areas: the atomic-scale behaviour of water and other liquids; and molecular processes at surfaces. I stress that the new methods are still evolving rapidly and I point to likely developments in the next few years.