Thin-walled aerospace components exhibit low structural stiffness, high aspect ratios and complex residual stress fields originating from forming, heat treatment and previous machining operations. As a consequence, these parts are highly susceptible to elastic deformation, chatter and post-machining distortion. Fixturing design plays a central role in controlling such phenomena and ensuring dimensional accuracy, surface integrity and process stability. This paper presents a structured review of fixturing design methodologies for thin-walled aerospace components, with particular emphasis on approaches that explicitly or implicitly consider complex stress states during machining. Based on 50 publications from 1990 to 2025, the review covers: (I) classical and computer-aided fixture design frameworks; (II) finite-element-based modelling of deformation and residual stresses; (III) fixture layout optimization methods; (IV) adaptive and intelligent fixturing systems; (V) additive-manufactured and topology-optimized fixtures; and (VI) digital-twin and AI-driven design strategies. The analysis indicates a clear evolution from rule-based fixture design towards integrated, model-driven and data-driven methodologies that couple finite element analysis, optimization algorithms, sensor feedback and digital twins. Remaining challenges include high computational cost, limited multi-physics integration, incomplete modelling of evolving residual stresses and the need for robust validation on full-scale aerospace structures. The paper concludes by highlighting research gaps and proposing future directions for holistic, stress-aware fixturing strategies.