The objective of this research effort was to demonstrate the path to continuous wave, coherent beam combination through stimulated Brillouin scattering phase conjugation in optical fiber. This work experimentally determined the fiber parameters necessary for phase conjugation in step-index optical fiber. Continuous wave phase conjugation using stimulated Brillouin scattering in step-index fibers was achieved for the first time with a fidelity of 0.8 and a threshold power of 16 W in a 15-m fiber with 0.13 NA. A fidelity of 0.8 was also achieved using 40 m of fiber with 0.06-NA and a threshold power of 15 W. The fidelity of phase conjugation was found to decline by 45% in an additional 20 m of 0.13-NA fiber and by 15% in 20 m of the 0.06-NA fiber. The effective Brillouin gain coefficient of the multimode fibers was found to vary directly with fidelity. A new technique using interference to measure fidelity was tested, and stimulated Brillouin scattering in a 2.5-km, graded-index fiber was found to produce beam cleanup to the fundamental fiber mode of the fiber with fidelity less than 0.1. This work demonstrated that coherent beam combining via continuous wave phase conjugation in optical fiber is achievable.