We present a comprehensive review of methods and applications of molecular simulations of interfacial systems. We give a detailed overview of the main techniques and major challenges in the following aspects of solid and fluid surfaces: adsorption at solid surfaces, interfacial transport and surface-to-bulk partitioning. We summarise methods to estimate macroscopic properties interfaces (adsorption isotherms, surface tension and contact angle) and ways to extract quantitative information about fluctuating liquid surfaces. We demonstrate the usage of these methods on recent applications from the fields of atmospheric science, material science and biophysics. The two main goals of this review are: (i) to provide guidance in practical questions, such as choosing software, force field, level of theory, system geometry, and finding the appropriate selective surface analysis methods based on the type of the interface and the nature of the physical problem to be studied; and (ii) to highlight domains where molecular simulations can bring about substantial advances in our understanding in important questions of applied science as a function of future method development and adaptation for applied fields.