8 pages, 3 figures; espcrc1 style; Invited Talk given at IX Int.Conf. on Nucleus-Nucleus Collisions, Rio de Janeiro Aug.2006; submitted to Nucl.Phys.AThe influence on the fusion process of coupling to collective degrees of freedom has been explored. The significant enhancement of the fusion cross section at sub-barrier energies was compared to predictions of one-dimensional barrier penetration models. This was understood in terms of the dynamical processes arising from strong couplings to collective inelastic excitations of the target and projectile. However, in the case of reactions where at least one of the colliding nuclei has a sufficiently low binding energy, for breakup to become an important process, conflicting model predictions and experimental r1esults have been reported in the literature. Excitation functions for sub- and near-barrier total (complete + incomplete) fusion cross sections have been measured for the $^{6,7}$Li+$^{59}$Co reactions. Elastic scattering as well as breakup/transfer yields have also been measured at several incident energies. Results of Continuum-Discretized Coupled-Channel (Cdcc) calculations describe reasonably well the experimental data for both reactions at and above the barrier. A systematic study of $^{4,6}$He induced fusion reactions with a three-body Cdcc method is presented. The relative importance of breakup and bound-state structure effects on total fusion (excitation functions) is particularly investigated. The four-body Cdcc model is being currently developed