Sustainable Supply Chain have become a cornerstone to any company that seeks to achieve sustainable goals. A company's image is no longer related to the old paradigm of being sustainable in its own activities, but instead is associated with a strong collaboration between all supply chain stakeholders, towards a sustainable activity. It is then critical to create new methods and tools to account for the three pillars of sustainability: economic, environmental and social, in a multi-stakeholder chain. In this context, operational research (OR) methods play a key role in supporting sustainable supply chain activities. This paper aims to review the trends and directions of OR methods applications towards the achievement of sustainable supply chain. A set of 220 papers has been reviewed to identify the OR methods being employed, the levels of decision considered and how sustainability practices were treated through OR. We found that optimization models applied to strategic level decisions are the most preponderant studies. Moreover, it was verified that sustainability has been mainly tackled by assessing economic and environmental aspects, leaving behind the social aspects. Additionally, OR-based studies do not yet present a clear definition of sustainability, a fact that is proven by the number of environmental and social methodologies explored. Based on the major trends identified in the literature, a research framework is derived, pointing towards a future research agenda in the area.