Laser Additive Manufacturing (LAM) involves complex laser-matter interactions characterized by extreme non-equilibrium thermodynamic processes. During this process, localized high-energy heat input and rapid cooling establish a highly non-uniform temperature field within the material. The interplay between severe temperature gradients and the material's thermal expansion and contraction behavior inevitably leads to the accumulation of significant residual stresses within the fabricated component. The presence of these internal stresses not only induces component warping and compromises geometric precision but also acts as a driving force for micro-crack propagation. This severely degrades fatigue life, fracture toughness, and corrosion resistance, thereby posing potential risks to structural safety during service. Consequently, the effective mitigation of residual stress has become a critical bottleneck restricting the large-scale application of LAM technology in high-end manufacturing sectors such as aerospace and biomedicine. This paper first elucidates the fundamental nature, classification system, and thermo-mechanical coupling origins of residual stress. It then systematically reviews multi-dimensional characterization techniques and the effects of key process parameters. Finally, integrating recent research advancements, it provides an in-depth analysis of the mechanisms, merits, limitations, and future trends of existing control strategies.