Synthetic polymers have been an integral part of modern society since the early 1960s. Besides their most well-known applications to the public, such as packaging, construction, textiles and electronics, synthetic polymers have also revolutionized the field of medicine. Starting with the first plastic syringe developed in 1955 to the complex polymeric materials used in the regeneration of tissues, their contributions have never been more prominent. Decades of research on polymeric materials, stem cells, and three-dimensional printing contributed to the rapid progress of tissue engineering and regenerative medicine that envisages the potential future of organ transplantations. This perspective discusses the role of synthetic polymers in tissue engineering, their design and properties in relation to each type of application. Additionally, selected recent achievements of tissue engineering using synthetic polymers are outlined to provide insight into how they will contribute to the advancement of the field in the near future. In this way, we aim to provide a guide that will help scientists with synthetic polymer design and selection for different tissue engineering applications.