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Density functional theory has become the workhorse of modern electronic structure cal- culations, with wide-ranging applications in chemistry, physics, materials science, biochem- istry, etc. At its heart lies the exchange- correlation functional, a quantity which exactly encapsulates the many-body effects stemming from the quantum mechanical interactions be- tween the electrons. Yet, the exact functional is unknown, and computationally tractable ap- proximations are therefore necessary for prac- tical applications. Over the past six decades, hundreds of density functional approximations have been proposed with varying degrees of ac- curacy and computational efficiency. This review surveys the theoretical founda- tions of semi-local functionals, including local density approximations, generalized gradient approximations, and meta-generalized gradient approximations. We provide a comprehensive, consistently organized discussion that consoli- dates both historical developments and recent advances in this field. Beginning with the es- sential concepts of Kohn–Sham density func- tional theory, we present the construction prin- ciples of semi-local exchange-correlation func- tionals. Special attention is given to the phys- ical motivations underlying functional develop- ment, the mathematical properties that guide their construction, and the practical consider- ations that determine their applicability across different chemical and physical systems. For each class of functionals, we trace their evo- lution from early prototypes to modern so- phisticated forms, highlighting key innovations and the interplay between theoretical rigor and empirical fitting. We examine how successive rungs of Jacob’s ladder, from the local den- sity approximation through generalized gradi- ent approximations to meta-generalized gradi- ent approximations, incorporate additional in- gredients to improve accuracy while maintain- ing computational efficiency. This work is intended to serve as both a in- troduction for newcomers to the field and a comprehensive reference for practitioners. By consolidating the extensive literature on semi- local functionals and providing a unified frame- work for understanding their construction and application, we aim to facilitate further devel- opments in density functional approximations and their use in tackling the diverse challenges of modern computational chemistry and con- densed matter physics.