Statistical models can be used as surrogates of detailed simulation models. Their key advantage is that they are evaluated at low computational cost which can remove computational barriers in building performance simulation. This comprehensive review discusses significant publications in sustainable building design research where surrogate modelling was applied. First, we familiarize the reader with the field and begin by explaining the use of surrogate modelling for building design with regard to applications in the conceptual design stage, for sensitivity and uncertainty analysis, and for building design optimisation. This is complemented with practical instructions on the steps required to derive a surrogate model. Next, publications in the field are discussed and significant methodological findings highlighted. We have aggregated 57 studies in a comprehensive table with details on objective, sampling strategy and surrogate model type. Based on the literature major research trends are extracted and useful practical aspects outlined. As surrogate modelling may contribute to many sustainable building design problems, this review summarizes and aggregates past successes, and serves as practical guide to make surrogate modelling accessible for future researchers. (C) 2019 Elsevier B.V. All rights reserved.