Tissue engineering is often referred to as a three-pronged discipline, with each prong corresponding to 1) a 3D material matrix (scaffold), 2) drugs that act on molecular signaling, and 3) regenerative living cells. Herein we focus on reviewing advances in controlled release of drugs from tissue engineering platforms. This review addresses advances in hydrogels and porous scaffolds that are synthesized from natural materials and synthetic polymers for the purposes of controlled release in tissue engineering. We pay special attention to efforts to reduce the burst release effect and to provide sustained and long-term release. Finally, novel approaches to controlled release are described, including devices that allow for pulsatile and sequential delivery. In addition to recent advances, limitations of current approaches and areas of further research are discussed.