The long standing problem of the infra-red divergence in quantum electrodynamics is reexamined in the light of the recent progress in this field. A general proof is given of the cancellation of the infrared divergences which arise from real and virtual processes. This proof is valid to all orders of the coupling constant and for all types of scattering events. The problem is solved in the iteration solution as well as in the closed form used by Bloch and Nordsieck and by Pauli and Fierz. The equivalence of the two methods is discussed and the results obtained by Bloch and Nordsieck are found to be correct provided radiative corrections are ignored. The ultraviolet divergences found by Pauli and Fierz in this connection has nothing to do with the infra-red divergence problem. It cannot be regarded as a difficulty in the theory, since the method of calculation employed is no longer valid at high frequencies. The exact calculation (iteration solution) shows that the renormalized theory is completely free of divergences at both low and high frequencies. A plausibility argument for the convergence in certain cases of the renormalized iteration solution is presented.