This article reviews the literature on multidimensional heat conduction in single fins and fin assemblies. The surface heat dissipation mechanisms include pure convection pure radiation, and simultaneous convection and radiation. Two-dimensional heat transfer results are presented for longitudinal, radial, and cylindrical fins. The discussion also covers square and polygonal fins on round tubes and composite fins. These heat transfer results encompass a variety of situations, such as a nonconstant base temperature, nonuniform ambient temperature, asymmetric thermal boundary conditions, anisotropy of fin material, variable heat transfer coefficient, and internal heat generation. The article provides a comprehensive collection of important analytical and numerical results for two-dimensional effects in extended surfaces, and, as such, both scientific and practice-oriented heat transfer workers would find the information convenient to use for analysis and design.