Computer-aided diagnosis (CAD) of prostate cancer on multiparametric magnetic resonance imaging (mpMRI), using artificial intelligence (AI), may reduce missed cancers and unnecessary biopsies, increase inter-observer agreement between radiologists, and alleviate pressures caused by rising case incidence and a shortage of specialist radiologists to read prostate mpMRI. However, well-designed evaluation studies are required to prove efficacy above current clinical practice. A systematic search of the MEDLINE, EMBASE, and arXiv electronic databases was conducted for studies that compared CAD for prostate cancer detection or classification on MRI against radiologist interpretation and a histopathological reference standard, in treatment-naïve men with a clinical suspicion of prostate cancer. Twenty-seven studies were included in the final analysis. Due to substantial heterogeneities in the included studies, a narrative synthesis is presented. Several studies reported superior diagnostic accuracy for CAD over radiologist interpretation on small, internal patient datasets, though this was not observed in the few studies that performed evaluation using external patient data. Our review found insufficient evidence to suggest the clinical deployment of artificial intelligence algorithms at present. Further work is needed to develop and enforce methodological standards, promote access to large diverse datasets, and conduct prospective evaluations before clinical adoption can be considered.