  In this review, we discuss the calculation of the $B\to P,V$ form factors
within the framework of the light-cone sum rules with the light-cone
distribution amplitudes of the $B$ meson. A detailed introduction to the
definition, scale evolution, and phenomenological models of the $B$-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 the $B\to
P,V$ form factors especially the contributions from the higher-twist $B$-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 element $|V_{ub}|$.
