The apparel supply chain is an example of a complex global supply chain where sustainability issues are a concern and where no satisfactory answers have been achieved yet, especially in social aspects. The growth in importance of social sustainability represents a strategic change in the sector with the necessary involvement of different tiers and external stakeholders to mitigate the negative social impacts. In this paper, a qualitative analysis through the application of content analysis using NVivo software is carried out, first to identify the structure and the main entities in this supply chain, and then to understand the main drivers towards social sustainability management. Six global companies were analysed, considering their sustainability reports from 2014 to 2018. The findings showed that social sustainability is a part of strategic goals as policies and commitments, and several actions have been developed along the supply chain to promote human rights, labour conditions, social development, and product responsibility, with external stakeholders collaboration. Finally, this article contributes to understanding how social sustainability should be managed in the apparel sector in a global supply chain context. Furthermore, in order to enrich the knowledge on this field, this paper provides some insight throughout the definition of a roadmap for future research in the area.