This paper presents a review of clustering and mathematical programming methods and their impacts on cell forming (CF) and scheduling problems. In-depth analysis is carried out by reviewing 105 dominant research papers from 1972 to 2017 available in the literature. Advantages, limitations and drawbacks of 11 clustering methods in addition to 8 meta-heuristics are also discussed. The domains of studied methods include cell forming, material transferring, voids, exceptional elements, bottleneck machines and uncertain product demands. Since most of the studied models are NP-hard, in each section of this research, a deep research on heuristics and metaheuristics beside the exact methods are provided. Outcomes of this work could determine some existing gaps in the knowledge base and provide directives for objectives of this research as well as future research which would help in clarifying many related questions in cellular manufacturing systems (CMS)
