Abstract: In system synthesis, we transform a desired specification into a system that is guaranteed to satisfy the specification. The talk will survey the development of synthesis algorithms for reactive systems. We will start with specification formalisms and how they have been developed from classical logic, continue to early work on synthesis of closed systems (systems that do not interact with an environment, making the synthesis problem similar to the satisfiability problem), and will reach synthesis of open systems (systems that interact with an environment, making the synthesis problem similar to the problem of generating winning strategies in two-player games). The talk assumes no previous knowledge in specification and synthesis.