Cardiovascular diseases remain the leading cause of mortality in many countries. Devices such as stents, vascular grafts, and heart valves have been developed to treat such diseases. However, many of these devices fail due to thrombotic complications. Recently, the fields of cardiovascular tissue engineering and regenerative medicine have begun to focus on treatments that not only replace diseased tissue, but also aid in the recovery and growth of new healthy tissue. Providing the appropriate matrix for tissue growth is essential to achieving effective tissue engineering solutions. Natural matrix materials can be advantageous as they have high biocompatibility, and are most similar to the native extracellular environment. Additionally, synthetic matrix materials may also provide advantages, since they are easily customizable and provide scalability. This dissertation will discuss work aimed to guide cardiovascular tissue regeneration, using both synthetic and natural approaches. Since non-thrombogenicity is a key concern, a comprehensive review of nonthrombogenic approaches in cardiovascular bioengineering will be presented first. Next, a novel approach, known as in situ vascular tissue engineering is presented and explored as a treatment for replacing clogged blood vessels. Specifically, we investigated the efficacy of small-diameter vascular grafts composed of electrospun nano-to-microscale fibers with immobilized heparin and vascular endothelial growth factor (VEGF). Finally, we discuss the development and efficacy of a naturally derived, injectable amniotic membrane scaffold for treatment of myocardial infarction.