Abstract. Full-text article available at: https://doi.org/10.1016/j.ins.2019.07.036Cyber-physical-social systems (CPSSs) are leading digital revolutions in academia, industry and government. Due to the rise of big data analytics, tensor computations are currently used in CPSSs. With the increasing popularity of cloud computing or fog computing, big data in CPSSs are usually sent to clouds or fogs for computations. Recently, some studies about privacy-preserving computation have been conducted to address security concerns which enable data analysis and processing in cloud or fog environments in a privacy-preserving way. To fully understand the state-of-the-art advances and discover the research directions of this field, in this survey, both previous and current privacy-preserving schemes are comprehensively reviewed and studied. In addition, a novel privacy-preserving tensor computation framework, a case study, and several future research directions are presented for CPSSs.