Within the great variety of production scheduling problems that exist, the job shop scheduling problem (JSP) is one that has generated the largest number of studies. It has also earned a reputation for being notoriously difficult to solve. Nevertheless, the JSP illustrates at least some of the demands imposed by a wide array of real world scheduling problems. This chapter summarizes the well-known approaches—algorithmic and heuristic—to solve the single objective job shop problem. Attempts to tackle the multiobjective job shop are still relatively few.