We describe the behavior of the fusion, break-up, reaction cross sections and elastic scattering of weakly bound nuclei, at near and above barrier energies. The total fusion cross sections are not affected by the break-up process at this energy regime. The elastic break-up cross sections are important at energies close and above the Coulomb barrier, even in systems with light targets, and increase the reaction cross sections. We also show that the break-up process at near and sub-barrier energies is responsible for the vanishing of the usual threshold anomaly of the optical potential and gives rise to a new type of anomaly, named by us as break-up threshold anomaly.