The occurrence of dysfunctional aortic valves is increasing every year, and current replacement heart valves, although having been shown to be clinically successful, are only short-term solutions and suffer from many agonizing long-term drawbacks. The tissue engineering of heart valves is recognized as one of the most promising answers for aortic valve disease therapy, but overcoming current shortcomings will require multidisciplinary efforts. The use of a polymeric scaffold to guide the growth of the tissue is the most common approach to generate a new tissue for an aortic heart valve. However, optimizing the design of the scaffold, in terms of biocompatibility, surface morphology for cell attachments and the correct rate of degradation is critical in creating a viable tissue-engineered aortic heart valve. This paper highlights the bioengineering strategies that need to be followed to construct a polymeric scaffold of sufficient mechanical integrity, with superior surface morphologies, that is capable of mimicking the valve dynamics in vivo. The current challenges and future directions of research for creating tissue-engineered aortic heart valves are also discussed.