Wave effects in the gravitational lensing of electromagnetic radiation by compact objects in astrophysics are treated. In the regime where the influence of diffraction is severe, solutions of the wave equation appropriate for lensing in astrophysics (which is of the form of the Schroumldinger equation for Coulomb scattering) are obtained. In the WKB regime, previous formulations are refined and extended to the case in which a part of the source is directly behind the lensing mass. Wave effects tend to be largest for this geometry which requires that radiation at a caustic be treated. The autocorrelation function of the electric field and the related frequency dependence of the radiation are emphasized, in addition to the diffraction pattern, to measure the deviations from the solutions obtained in the approximation of geometrical optics. In contrast, gravitational lensing is independent of frequency in the usual treatment which is based upon geometrical optics. Numerical computations are performed to indicate how the wave effects depend upon the relevant parameters including especially the size of the source. Wave effects are most significant at radio frequencies and for lensing by stellar and planetary masses. The importance of wave effects is governed by the ratio of the Schwarzschild radius of the lensing mass to the wavelength of the radiation.