The influence on fusion of coupling to the breakup process is investigatedfor reactions where at least one of the colliding nuclei has a sufficiently lowbinding energy for breakup to become an important process. Elastic scattering,excitation functions for sub-and near-barrier fusion cross sections, andbreakup yields are analyzed for $^{6,7}$Li+$^{59}$Co. Continuum-DiscretizedCoupled-Channels (CDCC) calculations describe well the data at and above thebarrier. Elastic scattering with $^{6}$Li (as compared to $^{7}$Li) indicatesthe significant role of breakup for weakly bound projectiles. A study of$^{4,6}$He induced fusion reactions with a three-body CDCC method for the$^6$He halo nucleus is presented. The relative importance of breakup andbound-state structure effects on total fusion is discussed.
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