Mineral surfaces play a prominent role in a broad range of geological, environmental and technological processes. Understanding their precise atomic structure, their interaction with the aqueous environment or organic molecules, and their reactivity is of crucial importance. In a context where, unfortunately, very often, experiments are either difficult to carry out or to interpret, atomistic numerical simulations may provide unique and complementary information. In the last decade, they have largely benefited from the huge increase of computational resources, which makes it timely to summarize recent advances made in this field.