<p>Extended surfaces are often used in thermal systems to improve heat transfer by increasing the convective surface area. They are used in power systems, electronic cooling, refrigeration, heat exchangers, and car engines. Plate, square, rectangular, longitudinal, radial, needle, serrated, cylindrical, airfoil-shaped, triangular, strip, trapezoidal, spiral, circular, annular, and pin fins are the significant fin configurations that are thoroughly reviewed in this study. The previous analytical model, experimental data, and numerical simulation study provide an explanation of the performance of each type. Early investigations focused on fin efficiency and conduction using longitudinal, square, and rectangular fins. Radial and annular fins are suited for compact heat exchangers, whereas spiral, serrated, and strip fins promote convective heat transfer and turbulence. Turbulent and forced convection are explored in pin, needle, and cylindrical fins. For lightweight and aerodynamic efficiency, aerofoil, triangular, and trapezoidal fins have been investigated. Analytical methods are effective for simple geometries, while advanced numerical and computational models are being applied to complex fin structures, with experimental research used for validation. This comparative approach shows methodological tendencies and connects theoretical models to practical applications. This article is novel in that it links fin geometry with the most effective approach, laying the groundwork for advanced fin design and thermal management system analysis. By combining existing data to assess the pros, cons, and applications of several fins, this study identifies gaps and opportunities for improved heat transfer investigation.</p>