The formation of artificial organs with tissue engineering techniques is necessary to address the growing disparity between the supply and need for donor organs. For use in tissue engineering regenerative applications, biomaterials should be biocompatible, porous (to allow cellular infiltration, nutrient transport and waste removal), mechanically tunable (to match and maintain the intrinsic mechanical properties of the tissue through the healing process), biodegradable (to allow the tissue to develop as the material degrades), reproducible, easily prepared, and cell/tissue compatible. This review will focus on various biomaterial design considerations and their effect on regenerative outcomes. By adjusting material designs, including pore size and degradation kinetics, in combination with functionalization with cell-and tissue-specific factors, intrinsic properties of tissue constructs can be controlled to enhance remodeling and functional outcomes.