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In this review, we discuss the calculation of the $B\to P,V$ form factorswithin the framework of the light-cone sum rules with the light-conedistribution amplitudes of the $B$ meson. A detailed introduction to thedefinition, scale evolution, and phenomenological models of the $B$-mesondistribution amplitudes is presented. We show two equivalent approaches ofcalculating the next-to-leading order QCD corrections to the sum rules for theform factors, i.e., the method of regions and the step-by-step matching in thesoft-collinear effective theory. The power suppressed corrections to the $B\toP,V$ form factors especially the contributions from the higher-twist $B$-mesondistribution amplitudes are displayed. We also present numerical results of theform factors including both the QCD and the power corrections, andphenomenological applications of the predicted form factors such as thedetermination of the CKM matrix element $|V_{ub}|$.

$B\to P,V$ form factors with the $B$-meson light-cone sum rules