This chapter introduces basic concepts of numerical modelling of materials on the atomic scale. An atomic interaction potential is at the core of each simulation. Static energy calculations and molecular dynamics simulations are common approaches to study crystal defects, such as point defects, dislocations and grain boundaries, phase transitions and diffusion processes in solids and liquids. The application of these powerful methods to geological materials is demonstrated with a number of examples. An important challenge for the future appears to be the crossover between accurate and predictive atomic-scale models and the continuum scale at which material properties are conventionally described. Some recent developments in this field are discussed.