The method of continuum-discretized coupled-channels (CDCC) is applied to two nuclear astrophysics studies. One is the determination of the astrophysical factor S17(0) for the 7Be(p,γ)8B reaction from the analysis of 8B breakup by 208Pb at 52 A MeV. We obtain S17(0) = 20.9+2.0-1.9 eV b, which is significantly larger than the previous one, S17(0) = 18.9±1.8 eV b, determined from an analysis with the virtual photon theory. The difference between the two values is found to be due to the contributions from nuclear breakup and higher-order processes. The other application of CDCC is the re-evaluation of the triple-α reaction rate by directly solving the three-body Schrödinger equation. The resonant and nonresonant processes are treated on the same footing. An accurate description of the α-α nonresonant states significantly quenches the Coulomb barrier between the first two α-particles and the third α-particle. Consequently, the α-α nonresonant continuum states give a markedly larger contribution at low temperatures than that reported in previous studies. We find an increase in triple-α reaction rate by 26 orders of magnitude around 107 K compared with the rate of NACRE.