In this review, we discuss the calculation of theB⟶P,Vform factors within the framework of the light-cone sum rules with the light-cone distribution amplitudes of theB-meson. A detailed introduction to the definition, scale evolution, and phenomenological models of theB-meson distribution amplitudes is presented. We show two equivalent approaches of calculating the next-to-leading order QCD corrections to the sum rules for the form factors, i.e., the method of regions and the step-by-step matching in the soft-collinear effective theory. The power suppressed corrections to theB⟶P,Vform factors especially the contributions from the higher-twistB-meson distribution amplitudes are displayed. We also present numerical results of the form factors including both the QCD and the power corrections, and phenomenological applications of the predicted form factors such as the determination of the CKM matrix elementVub.