Diphenyl carbonate is one of the raw materials used for the synthesis of polycarbonate, and its green and clean production is of great importance to the non-phosgene process for polycarbonate. The production of diphenyl carbonate by transesterification is its representative process route and is considered to be one of the typical examples of a green and sustainable process for chemicals. Since the discovery of the transesterification catalyst for diphenyl carbonate in the 1970s, researchers have been committed to improving its catalytic activity and selectivity and, correspondingly, the reaction engineering process. However, thermodynamic limitations, low activity, low selectivity, and limited stability have been bottlenecks that the transesterification catalyst has not been able to completely overcome, and the improvement of the catalyst is still ongoing. Therefore, this review takes the transesterification reaction of dimethyl carbonate and phenol as a model reaction and, based on a review of the progress in catalyst research on catalytic reaction processes, tries to clarify the structure–activity relationship between catalytic active sites and catalytic performance in homogeneous and heterogeneous catalytic processes and provides an overview of the progress in catalyst synthesis and modification.