Ferroelectric transistors (FeFETs) based on doped hafnium oxide (HfO2) have received much attention due to their technological potential in terms of scalability, high-speed, and lowpower operation. Unfortunately, however, HfO2-FeFETs also suffer from persistent reliability challenges, specifically affecting retention, endurance, and variability. There is a broad consensus that a deep understanding of the reliability physics of HfO2-FeFETs is an essential prerequisite for the successful commercialization of this promising technology. In this paper, we review the current understanding of the relevant reliability aspects of HfO2-FeFETs. We initially focus on the reliability physics of ferroelectric capacitors, as a prelude to a comprehensive analysis of FeFET reliability. Then, we interpret key reliability metrics of the FeFET at device-level (i.e., retention, endurance, variability) based on the physical mechanisms previously identified. Our integrative theoretical framework connects apparently unrelated reliability issues and suggests mitigation strategies at either device, circuit, and system level. We conclude the paper by proposing a set of research opportunities to guide future development in this field.