This paper points out the significance of cooling in injection molding and briefly reviews the development of cooling systems. The focus of this survey is on the physical model, development, and optimization of conformal cooling systems which have curved cooling circuits following the shape of mold cavity. Compared with traditional cooling systems, conformal cooling can greatly reduce the warpage defect and shorten the cooling cycle time. The computational design methods and additive manufacturing techniques that prompt the development of conformal cooling are deeply investigated. At the end of this survey, the future perspectives for conformal cooling design and manufacturing are discussed.