The technological choices facing organisations are increasingly complex and aimed at promoting sustainable development. Recently, the concept of Industry 5.0 has laid the foundations for a digital transformation that drives companies to adopt sustainable approaches. Although there are various contributions investigating the link between sustainable production and digital technologies, there is still a lack of comprehensive research on the role of digital technologies in achieving the three pillars of sustainability in specific areas of supply chain management (SCM). The article aims to assess and understand which digital technologies are the most promising for achieving sustainability standards. Through a systematic literature review, the study analyses 1,720 scientific articles that identify business practices supported by digital technologies such as: 3D printing, artificial intelligence, blockchain, computing, digital applications, geospatial technologies, immersive environments, Internet of Things, open and crowd-based platforms, proximity technologies and robotics. Such business practices are thereafter associated with specific areas of SCM such as distribution, marketing and procurement. The results show that blockchain technology is promising for different sustainability aspects, whereas computing, 3D printing and immersive environments are less employed for sustainable development. The study also highlights that scholars have paid more attention to environmental rather than economic and social sustainability dimensions. The contribution of this article is to provide a current overview of digital technologies in SCM to clarify the state of the art of research. It also defines a research agenda for academics to conduct further exploratory research. For managers and practitioners, it presents a knowledge base where data on sustainable practices supported by digital technologies in SCM have been collected and organised, providing information to companies on opportunities for implementation in their own business.