With the advancement of new material technologies and the invention of new techniques such as 3D printing over recent decades, the fabrication of more complex and versatile structures from biocomposites can now be easily achieved. Graphenic fillers are being increasingly used to improve and tune the electrical conductivity and mechanical properties of biodegradable/biocompatible polymers thus opening the way for the fabrication of biocomposite structures critical for areas such as tissue engineering. This review provides an overview of recent work on the fabrication of structures using graphene-based biocomposites, which provide constructs with properties better tailored to a variety of biomedical applications.