Translation quality assessment (TQA) represents one of the most productive lines of research in Translation Studies (TS), with scholars proposing different TQA models. In parallel to these theoretical models is the emergence of a diverse array of assessment methods trialled and used to evaluate translation quality in different. Despite these developments, it seems that little effort has been made to bring to the fore methodological aspects of the TQA practices. This methodological review sets out to track the developmental trend of the TQA methods, hoping to bring clarity to the nature of the methodological pluralism, driving forces behind methodological evolution, as well as promises and constraints of each methodological choice. The review also attempts to interrogate the TQA practices, focusing on three overarching issues of reliability, validity and practicality. By doing so, we hope to highlight their merits and demerits, and occasionally challenge their legitimacy. Finally, the review describes some gaps in TQA practice and research, and suggests potential directions to move forward the enterprise of TQA.