The current state of healthcare in the world is dire, with millions of people unable to access healthcare services on time. One of the key reasons behind this problem is the lack of operational efficiency in many clinics and hospitals, caused due to unscientific scheduling practices. Hence, this paper seeks to conduct a systematic review of the existing research done in the field of healthcare service scheduling, and its multiple sub-sections viz. appointment scheduling, nurse rostering, home healthcare scheduling, etc. The bibliometric review found that majority of the research in the aforementioned field is scattered and lacks integration. Moreover, past research has primarily employed matheuristics, mixed integer linear programming and simulation approaches to solve service scheduling problems, without exploring other methods to a great extent. In the end, we suggest some topics in which future research can be conducted.