Quality assurance is a central component of human and machine translation. In translation studies, translation quality focuses on human evaluation and dimensions, such as purpose, comprehensibility, target audience among many more. Within the field of machine translation, more operationalized definitions of quality lead to automated metrics relying on reference translations or quality estimation. A joint approach to defining and assessing translation quality holds the promise to be mutually beneficial. To contribute towards that objective, this systematic survey provides an interdisciplinary analysis of the concept of translation quality from both perspectives. Thereby, it seeks to inspire cross-fertilization between both fields and further development of an interdisciplinary concept of translation quality.