This literature review provides an in-depth exploration of the research conducted on residual stresses (RS) in Wire Arc Additive Manufacturing (WAAM) products, particularly focusing on how process parameters influence the phenomenon. The motivation of the study is the growing focus on WAAM technology and the observation that RS plays a crucial role in determining the mechanical behavior and structural integrity of WAAM components. Thus, the review is intended to provide a better understanding of the relationship between process parameters and RS to optimize the WAAM process and ensure the durability of the final products. It also summarizes key findings, measurement techniques, challenges, and future directions in this evolving field. The review also analyzes measurement techniques used to characterize RS in products fabricated by WAAM as a function of process parameters. Experimental measuring techniques and numerical analysis of RS to determine the impacts of RS in mechanical responses in products of WAAM were discussed. Experimental measuring techniques, such as X-ray diffraction, neutron diffraction (ND), contour and ND, digital image correlation, thermomechanical coupling and contour, and hole-drilling methods, along with numerical simulations like finite element analysis, are discussed to determine the impacts of RS on the mechanical responses of WAAM products. Additionally, it addresses the influence of thermal cycles, cooling rates, and deposition strategies on RS formation. The role of material properties, such as thermal conductivity and expansion coefficients, in RS development is also considered. By offering a comprehensive overview of current research trends and insights, this review serves as a valuable resource to guide future investigations, fostering the advancement of WAAM as a robust and efficient manufacturing technology. The review also underscores the importance of interdisciplinary approaches combining experimental and numerical methods to tackle the complex issues of RS in WAAM, aiming to enhance the performance and reliability of additively manufactured components.