Incremental sheet forming has emerged as an excellent alternative to other material forming procedures, incrementally deforming flat metal sheets into complex three-dimensional profiles. The main characteristics of this process are its versatility and cost-effectiveness; additionally, it allows for greater formability compared to conventional sheet forming processes. Recently, its application has been extended to polymers and composites. The following review aims to present the current state of the art in the incremental sheet forming of polycarbonate, an outstanding engineering plastic, beginning with initial studies on the feasibility of this process for polymers. Attention is given to the advantages, drawbacks, and main applications of incrementally formed polycarbonate sheets, as well as the influence of process parameters and toolpath strategies on features such as formability, forming forces, deformation and failure mechanisms, geometric accuracy, surface quality, etc. Additionally, new hybrid forming methods for process optimisation are presented. Finally, a discussion is provided on the technical challenges and future research directions for incremental sheet forming of polycarbonate and, more generally, thermoplastics. Thus, this review aims to offer an extensive overview of the incremental forming of polycarbonate sheets, useful to both academic and industrial researchers working on this topic.