The development of a novel artificial heart valve with outstanding durability and safety has remained a challenge since the first mechanical heart valve entered the market 65 years ago. Recent progress in high-molecular compounds opened new horizons in overcoming major drawbacks of mechanical and tissue heart valves (dysfunction and failure, tissue degradation, calcification, high immunogenic potential, and high risk of thrombosis), providing new insights into the development of an ideal artificial heart valve. Polymeric heart valves can best mimic the tissue-level mechanical behavior of the native valves. This review summarizes the evolution of polymeric heart valves and the state-of-the-art approaches to their development, fabrication, and manufacturing. The review discusses the biocompatibility and durability testing of previously investigated polymeric materials and presents the most recent developments, including the first human clinical trials of LifePolymer. New promising functional polymers, nanocomposite biomaterials, and valve designs are discussed in terms of their potential application in the development of an ideal polymeric heart valve. The superiority and inferiority of nanocomposite and hybrid materials to non-modified polymers are reported. The review proposes several concepts potentially suitable to address the above-mentioned challenges arising in the R&D of polymeric heart valves from the properties, structure, and surface of polymeric materials. Additive manufacturing, nanotechnology, anisotropy control, machine learning, and advanced modeling tools have given the green light to set new directions for polymeric heart valves.