This chapter presents an introduction to surface astrochemistry. It provides an overview of the extensive laboratory investigations of molecular hydrogen formation on carbonaceous surfaces ranging from graphite to mixtures of aliphatic or aromatic flame-deposited surfaces. These investigations have resulted in insights into often complex formation mechanisms operating in all these different systems. The chapter outlines the influence of water ice morphology on desorption of surface species and on surface reactions, as well as the influence of surface reactions on the water ice morphology. Moving beyond molecular hydrogen formation, the chapter provides an overview of the current state of the art in laboratory studies of complex molecule formation on interstellar surface analogs. Finally, an overview of the challenges and current state of the art for implementing grain surface reactions in astrochemical network models is given.