Tissue engineering scaffolds are designed to mimic physical, chemical, and biological features of the extracellular matrix, thereby providing a constant support that is crucial to improved regenerative medicine outcomes. Beyond mechanical and structural support, the next generation of these materials must also consider the more dynamic presentation and delivery of drugs or growth factors to guide new and regenerating tissue development. These two aspects are explored expansively separately, but they must interact synergistically to achieve optimal regeneration. This review explores common tissue engineering materials types, electrospun polymers and hydrogels, and strategies used for incorporating drug delivery systems into these scaffolds.