High-power operation of fiber lasers was mainly enabled by the invention of cladding-pumping in a double-clad fiber structure. Pump absorption is enhanced by broken circular symmetry of inner cladding cross-sections and by mode-scrambling of the pump modes resulting from unconventional fiber coiling. However, theoretical studies were limited to the assumption of a straight fiber until recently, when the rigorous model accounting for double-clad fiber bending and twisting was described. It was found that squeezing of the effective area of the pump radiation due to fiber bending plays an important role in cladding-pump absorption enhancement. We review results of numerical modeling of pump absorption in various types of double-clad fibers, e.g., with cross-section shape of hexagon, stadium, and circle; two-fiber bundle (so-called GTWave fiber structure) a panda fibers are also analyzed. The presented results can have a practical application and potential impact in the construction of fiber lasers: with pump absorption efficiency optimized by our new model (the other models did not take into account fiber twist), the double-clad fiber of shorter length can be used in the fiber lasers and amplifiers. This dramatically minimizes the deleterious effect of background losses and nonlinear effects. © 2019 IEEE.