In this paper we discuss mathematical, numerical and atomistic models of growth at surfaces through a number of examples. It is shown how such models have often been successful in predicting the structures that are observed experimentally. Different kinds of models are often complementary to each other. Mathematical models can give guidance on the long-time behaviour of the system but often need help from more detailed simulation to decide what to assume about the underlying microscopic processes. Despite their success, such models still have a long way to go. In particular, they need to address the question of how to predict the effective properties of coatings. Here experimental data are not always available, and guidance from theory is greatly needed.