Shape memory materials, specifically nickel-titanium alloys, are used in a number of minimally invasive clinical procedures demonstrating significant improvements in clinical outcomes and standard of care compared to open procedures. However, concerns regarding erosion events, device failure, and consequent morbidities are driving interest in tissue engineering approaches which support or stimulate the patient's own tissue regenerative processes to repair and regenerate tissues. Growing interest in addressing these challenges using minimally invasive procedures is driving the rapid advancement of a new class of materials; biodegradable shape memory polymers (SMPs). These biodegradable SMPs are designed for compaction and delivery through keyhole incisions, expansion when they reach the target tissue, maintenance of mechanical continuity with surrounding tissues upon implantation, attachment of regenerative cells driving tissue growth and infiltration, and degradation into nontoxic byproducts. Polyesters are predominantly used in the design of these SMPs to impart biodegradability through hydrolysis. Use of homopolymers, copolymers, terpolymers, block-copolymers, and interpenetrating networks has given rise to a range of SMPs spanning applications from endovascular to bone defect repair. Translating these materials to the clinic and applying these materials toward patient specific design can advance the current standard of care across various clinical disciplines.