  The 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
results 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 ({\sc 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 {\sc 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 {\sc Cdcc} model is being currently
developed.
