A closed-loop supply chain (CLSC) has been defined as a path that the material flows, starting from suppliers till it arrives at customers as a final product, including product recovery from customers to manufacturers for various usages. A stochastic CLSC handles uncertainty in critical parameters that affect CLSC design. This novel study presents a stochastic CLSC review and categorises uncertainty types applied to stochastic parameters under analysis. Also, the study describes various algorithms that are suitable for solving the different stochastic CLSC models. The research benefits practitioners and researchers by creating guidelines for stochastic CLSC design and discusses the strengths and weaknesses of algorithms used. The results showed the significance of a hybrid genetic, particle swarm optimisation (hybrid GA-PSO) in optimising constrained stochastic CLSC models and the advancement of stochastic CLSC research in the automotive industry. Future research should explore more uncertain parameters, methods of modelling social aspects, and new strategies to implement in stochastic CLSC.