On-surface synthesis constitutes a rapidly growing field of research due to its promising application for creating stable molecular structures on surfaces. While self-assembled structures rely on reversible interactions, on-surface synthesis provides the potential for creating long-term stable structures with well-controlled properties, for example superior electron transport for future molecular electronic devices. On-surface synthesis holds the promise for preparing insoluble compounds that cannot be produced in solution. Another highly exciting aspect of on-surface synthesis is the chance to discover new reaction pathways due to the two-dimensional confinement of the reaction educts. In this review, we discuss the current state-of-the-art and classify the reactions that have been successfully performed so far. Special emphasis is put on electrically insulating surfaces, as these substrates pose particular challenges for on-surface synthesis while at the same time bearing high potential for future use, for example, in molecular electronics.