Organ-on-A-chip (OoAC) devices are miniaturized, functional, in vitro constructs that aim to recapitulate the in vivo physiology of an organ using different cell types and extracellular matrix, while maintaining the chemical and mechanical properties of the surrounding microenvironments. From an end-point perspective, the success of a microfluidic OoAC relies mainly on the type of biomaterial and the fabrication strategy employed. Certain biomaterials, such as PDMS (polydimethylsiloxane), are preferred over others due to their ease of fabrication and proven success in modelling complex organ systems. However, the inherent nature of human microtissues to respond differently to surrounding stimulations has led to the combination of biomaterials ranging from simple PDMS chips to 3D-printed polymers coated with natural and synthetic materials, including hydrogels. In addition, recent advances in 3D printing and bioprinting techniques have led to the powerful combination of utilizing these materials to develop microfluidic OoAC devices. In this narrative review, we evaluate the different materials used to fabricate microfluidic OoAC devices while outlining their pros and cons in different organ systems. A note on combining the advances made in additive manufacturing (AM) techniques for the microfabrication of these complex systems is also discussed.