So far, a vast amount of studies on sustainability in supply chain management have been conducted by academics over the last decade. Nevertheless, socially related aspects are still neglected in the related discussion. The primary motivation of the present literature review has arisen from this shortcoming, thus the key purpose of this study is to enrich the discussion by providing a state-of-the-art, focusing exclusively on social issues in sustainable supply chain management (SSCM) by considering the textile/apparel sector as the field of application. The authors conduct a literature review, including content analysis which covers 45 articles published in English peer-reviewed journals, and proposes a comprehensive map which integrates the latest findings on socially related practices in the textile/apparel industry with the dominant conceptualization in order to reveal potential research areas in the field. The results show an ongoing lack of investigation regarding the social dimension of the triple bottom line in SSCM. Findings indicate that a company’s internal orientation is the main assisting factor in sustainable supply chain management practices. Further, supplier collaboration and assessment can be interpreted as an offer for suppliers deriving from stakeholders and a focal company’s management of social risk. Nevertheless, suppliers do also face or even create huge barriers in improving their social performance. This calls for more empirical research and qualitative or quantitative survey methods, especially at the supplier level located in developing countries.