Sustainability management in global fashion operations is an area of growing concern. This can be seen by the number of research articles and industrial reports published. To establish a further debate, this study pursues two objectives. Firstly, it provides a systematic literature review pertaining to environmental and social sustainability management in fashion operations by encompassing 38 research articles indexed in Scopus from 2006 to 2016. Secondly, it presents a classification framework in which sustainability practices are categorized according to a three-dimensional concurrent engineering framework by focusing on product, process and supply chain levels. Results address that the breakdown of environmental and social sustainability practices identified in earlier research is not homogenous. For instance, some critical social aspects such as human rights are not widely covered in production processes. Similarly, serious environmental aspects such as biodiversity are not entirely focused on at the chain level. Last, this study concludes with a framework illustrating strategic priorities to be taken to advance sustainability in fashion operations.