Congenital penile curvature (CPC) is a relatively uncommon condition, characterized by congenital angulation of the erect penis. Surgical correction of CPC is the gold standard therapy with a variety of proposed surgical techniques and modifications. This review summarizes the contemporary literature on the surgical management of CPC, trying to address the current trends, as well as the advantages and disadvantages of available methods. We performed a non-systematic narrative and interpretative literature review until December 2018. We included articles with isolated CPC in human adults. We excluded original research articles regarding the surgical treatment of Peyronie’s disease (PD). In total, we identified 34 studies including 2155 patients with CPC that met our inclusion criteria. Nine studies included patients with both CPC and PD, but reported sufficient data regarding the CPC cohort. Excisional corporoplasty and incisionless plication seemed to be the preferred surgical methods (10 and 12 studies, respectively), followed by incisional corporoplasty (5) and grafting (3). Four studies reported results of more than one method. Overall, patients with CPC can expect excellent outcomes with surgical repair and minimal side effects. No definite conclusions can be made regarding which technique is superior. The widely varied outcomes highlight the need for standardized outcomes measures in future research.