Background: This literature review delves into the concept of ‘Third-party Reverse Logistics selection’, focusing on its process and functionality using deterministic and uncertain decision-making models. In an increasingly globalized world, Reverse Logistics (RL) plays a vital role in optimizing supply chain management, reducing waste, and achieving sustainability objectives. Deterministic decision-making models employ predefined criteria and variables, utilizing mathematical algorithms to assess factors such as cost, reliability, and capacity across various geographical regions. Uncertain decision-making models, on the other hand, incorporate the unpredictability of real-world scenarios by considering the uncertainties and consequences of decision making and choices based on incomplete information, ambiguity, unreliability, and the option for multiple probable outcomes. Methods: Through an examination of 41 peer-reviewed journal publications between the years 2020 and 2023, this review paper explores these concepts and problem domains within three categories: Literature Reviews (LR), Deterministic Decision-Making (DDM) models, and Uncertain Decision-Making (UDM) models. Results: In this paper, observations and future research directions are discussed. Conclusions: This paper provides a comprehensive review of third-party reverse logistics selection papers.