Polycaprolactone (PCL) is an important polymer due to its mechanical properties, miscibility with a large range of other polymers and biodegradability. Two main pathways to produce polycaprolactone have been described in the literature: the polycondensation of a hydroxycarboxylic acid: 6-hydroxyhexanoic acid, and the ring-opening polymerisation (ROP) of a lactone: epsilon-caprolactone (epsilon-CL). This critical review summarises the different conditions which have been described to synthesise PCL, and gives a broad overview of the different catalytic systems that were used (enzymatic, organic and metal catalyst systems). A surprising variety of catalytic systems have been studied, touching on virtually every section of the periodic table. A detailed list of reaction conditions and catalysts/initiators is given and reaction mechanisms are presented where known. Emphasis is put on the ROP pathway due to its prevalence in the literature and the superior polymer that is obtained. In addition, ineffective systems that have been tried to catalyse the production of PCL are included in the electronic supplementary information for completeness (141 references).