The absence of pharmacological treatments to reduce or retard the progression of cardiac valve diseases makes replacement with artificial prostheses (mechanical or bio-prosthetic) essential. Given the increasing incidence of cardiac valve pathologies, there is always a more stringent need for valve replacements that offer enhanced performance and durability. Unfortunately, surgical valve replacement with mechanical or biological substitutes still leads to disadvantages over time. In fact, mechanical valves require a lifetime anticoagulation therapy that leads to a rise in thromboembolic complications, while biological valves are still manufactured with non-living tissue, consisting of aldehyde-treated xenograft material (e.g., bovine pericardium) whose integration into the host fails in the mid- to long-term due to unresolved issues regarding immune-compatibility. While various solutions to these shortcomings are currently under scrutiny, the possibility to implant fully biologically compatible valve replacements remains elusive, at least for large-scale deployment. In this regard, the failure in translation of most of the designed tissue engineered heart valves (TEHVs) to a viable clinical solution has played a major role. In this review, we present a comprehensive overview of the TEHVs developed until now, and critically analyze their strengths and limitations emerging from basic research and clinical trials. Starting from these aspects, we will also discuss strategies currently under investigation to produce valve replacements endowed with a true ability to self-repair, remodel and regenerate. We will discuss these new developments not only considering the scientific/technical framework inherent to the design of novel valve prostheses, but also economical and regulatory aspects, which may be crucial for the success of these novel designs.