In this paper, we discuss scheduling problems in semiconductor manufacturing. Starting from describing the manufacturing process, we identify typical scheduling problems found in semiconductor manufacturing systems. We describe batch scheduling problems, parallel machine scheduling problems, job shop scheduling problems, scheduling problems with auxiliary resources, multiple orders per job scheduling problems, and scheduling problems related to cluster tools. We also present important solution techniques that are used to solve these scheduling problems by means of specific examples, and report on known implementations. Finally, we summarize some of the challenges in scheduling semiconductor manufacturing operations.