With the advent of inexpensive and highly accurate 3D printing devices, a tremendous flurry of research activity has been unleashed into new resorbable, polymeric materials that can be printed using three approaches: hydrogels for bioprinting and bioplotting, sintered polymer powders, and solid cured (photocrosslinked) resins. Additionally, there is a race to understand the role of extracellular matrix components and cell signalling molecules and to fashion ways to incorporate these materials into resorbable implants. These chimeric materials along with microfluidic devices to study organs or create labs on chips, are all receiving intense attention despite the limited number of polymer systems that can accommodate the biofabrication processes necessary to render these constructs. Perhaps most telling is the limited number of photo-crosslinkable, resorbable polymers and fabrication additives (e.g., photoinitiators, solvents, dyes, dispersants, emulsifiers, or bioactive molecules such as micro-RNAs, peptides, proteins, exosomes, micelles, or ceramic crystals) available to create resins that have been validated as biocompatible. Advances are needed to manipulate 4D properties of 3D printed scaffolds such as pre-implantation cell culture, mechanical properties, resorption kinetics, drug delivery, scaffold surface functionalization, cell attachment, cell proliferation, cell maturation, or tissue remodelling; all of which are necessary for regenerative medicine applications along with expanding the small set of materials in clinical use. This manuscript presents a review of the foundation of the most common photopolymerizable resins for solidcured scaffolds and medical devices, namely, polyethylene glycol (PEG), poly(D, L-lactide) (PDLLA), poly-ε-caprolactone (PCL), and poly(propylene fumarate) (PPF), along with methodological advances for 3D Printing tissue engineered implants (e.g., via stereolithography [SLA], continuous Digital Light Processing [cDLP], and Liquid Crystal Display [LCD]).