Supply chain network design (SCND) models and methods have been the subject of several recent literature review surveys, but none of them explicitly includes sustainable development as a main characteristic of the problem considered. The aim of this review is to bridge this gap. The paper analyzes 87 papers in the field of supply chain network design, covering mathematical models that include economic factors as well as environmental and/or social dimensions. The review is organized along four research questions asking (i) which environmental and social objectives are included, (ii) how are they integrated into the models, (iii) which methods and tool are used and finally (iv) which industrial applications and contexts are covered in these models. The review finds that there are a number of limitations to the current research in sustainable SCND. The narrow scope of environmental and social measures in current models should go beyond limited greenhouse gas indicators to broader life-cycle approaches including new social metrics. The more effective inclusion of uncertainty and risk in models with improved multi-objective approaches is also needed. There are also significant gaps in the sectors used to test models limiting more general applicability. The paper concludes with promising new avenues of research to more effectively include sustainability into SCND models.