Potential applications of tissue engineering in regenerative medicine range from structural tissues to organs with complex function. This review focuses on the engineering of heart valve tissue, a goal which involves a unique combination of biological, engineering, and technological hurdles. We emphasize basic concepts, approaches and methods, progress made, and remaining challenges. To provide a framework for understanding the enabling scientific principles, we first examine the elements and features of normal heart valve functional structure, biomechanics, development, maturation, remodeling, and response to injury. Following a discussion of the fundamental principles of tissue engineering applicable to heart valves, we examine three approaches to achieving the goal of an engineered tissue heart valve: (1) cell seeding of biodegradable synthetic scaffolds, (2) cell seeding of processed tissue scaffolds, and (3) in-vivo repopulation by circulating endogenous cells of implanted substrates without prior in-vitro cell seeding. Lastly, we analyze challenges to the field and suggest future directions for both preclinical and translational (clinical) studies that will be needed to address key regulatory issues for safety and efficacy of the application of tissue engineering and regenerative approaches to heart valves. Although modest progress has been made toward the goal of a clinically useful tissue engineered heart valve, further success and ultimate human benefit will be dependent upon advances in biodegradable polymers and other scaffolds, cellular manipulation, strategies for rebuilding the extracellular matrix, and techniques to characterize and potentially non-invasively assess the speed and quality of tissue healing and remodeling.