We studied the phase and polarization properties of phase conjugation by degenerate four-wave mixing (DFWM). Dye-doped glasses were used as the nonlinear optical material in the experimental studies. The nonlinear optical response of these materials is due to saturable absorption. We have measured a third-order nonlinear optical susceptibility as large as 1 esu and a response time of approximately 0.1 sec for fluorescein-doped boric-acid glass at room temperature. Furthermore, we have demonstrated that the nonlinear optical response of this material can be enhanced by up to an order of magnitude through cooling; third-order susceptibilities as large as 10 esu have been measured when the sample is cooled sufficiently. We have also shown that lead-tin fluorophosphate glass doped with acridine yellow and acridine orange has faster response times and much better durability than fluorescein-doped boric-acid glass, but has slightly smaller nonlinearities. We used fluorescein-doped boric-acid glass as the nonlinear optical material in our experimental study of the properties of phase-conjugate signals generated through DFWM. </br>The saturation properties of dye molecules that are rigidly held in a solid matrix were exploited to achieve nearly perfect vector phase conjugation. We have studied these properties theoretically and experimentally. Further, we have demonstrated that DFWM can be successfully employed to remove the deleterious effects of most wavefront and polarization aberrations in double pass. However, the polarization distortions due to Faraday rotation cannot be corrected using optical phase conjugation. We have used a phase-conjugate interferometer to demonstrate that a phase-conjugate mirror based on DFWM determines the phase of the incident signal field with respect to the phases of the pump fields. </br>We have demonstrated a passive, one-way imaging system using four-wave mixing that corrects distortions incurred by an optical wavefront in passing through a thin phase aberrating medium. This method can be applied to situations that require the original object and corrected image be on opposite sides of the aberrator. </br>We have also performed experimental studies of a geometrical phase for optical systems containing a phase-conjugate mirror. We find that phase conjugation corrects for the geometrical phase of the system.