In situ heart valve tissue engineering using cell-free synthetic, biodegradable scaffolds is under development as a clinically attractive approach to create living valves right inside the heart of a patient. In this approach, a valve-shaped porous scaffold "implant" is rapidly populated by endogenous cells that initiate neo-tissue formation in pace with scaffold degradation. While this may constitute a cost-effective procedure, compatible with regulatory and clinical standards worldwide, the new technology heavily relies on the development of advanced biomaterials, the processing thereof into (minimally invasive deliverable) scaffolds, and the interaction of such materials with endogenous cells and neo-tissue under hemodynamic conditions. Despite the first positive preclinical results and the initiation of a small-scale clinical trial by commercial parties, in situ tissue formation is not well understood. In addition, it remains to be determined whether the resulting neo-tissue can grow with the body and preserves functional homeostasis throughout life. More important yet, it is still unknown if and how in situ tissue formation can be controlled under conditions of genetic or acquired disease. Here, we discuss the recent advances of material-based in situ heart valve tissue engineering and highlight the most critical issues that remain before clinical application can be expected. We argue that a combination of basic science - unveiling the mechanisms of the human body to respond to the implanted biomaterial under (patho)physiological conditions - and technological advancements - relating to the development of next generation materials and the prediction of in situ tissue growth and adaptation - is essential to take the next step towards a realistic and rewarding translation of in situ heart valve tissue engineering.