In this Review article pioneering work and recent achievements in the emerging research area of on-surface chemistry is discussed. On-surface chemistry, sometimes also called two-dimensional chemistry, shows great potential for bottom-up preparation of defined nanostructures. In contrast to traditional organic synthesis, where reactions are generally conducted in well-defined reaction flasks in solution, on-surface chemistry is performed in the cavity of a scanning probe microscope on a metal crystal under ultrahigh vacuum conditions. The metal first acts as a platform for self-assembly of the organic building blocks and in many cases it also acts as a catalyst for the given chemical transformation. Products and hence success of the reaction are directly analyzed by scanning probe microscopy. This Review provides a general overview of this chemistry highlighting advantages and disadvantages as compared to traditional reaction setups. The second part of the Review then focuses on reactions that have been successfully conducted as on-surface processes. On-surface Ullmann and Glaser couplings are addressed. In addition, cyclodehydrogenation reactions and cycloadditions are discussed and reactions involving the carbonyl functionality are highlighted. Finally, the first examples of sequential on-surface chemistry are considered in which two different functionalities are chemoselectively addressed. The Review gives an overview for experts working in the area but also offers a starting point to non-experts to enter into this exciting new interdisciplinary research field.