Graphene-based materials (GBM) are considered one of the 21st century’s most promising materials, as they are incredibly light, strong, thin and have remarkable electrical and thermal properties. As a result, over the past decade, their combination with a diverse range of synthetic polymers has been explored in tissue engineering (TE) and regenerative medicine (RM). In addition, a wide range of methods for fabricating polymer/GBM scaffolds have been reported. This review provides an overview of the most recent advances in polymer/GBM composite development and fabrication, focusing on methods such as electrospinning and additive manufacturing (AM). As a future outlook, this work stresses the need for more in vivo studies to validate polymer/GBM composite scaffolds for TE applications, and gives insight on their fabrication by state-of-the-art processing technologies.