The demand for network capacity has been steadily increasing in recent decades due to the growth of new digital applications and services. Optical fiber supports to solve and avoid data traffic bottlenecks when dealing with high capacity data rate requirements. When fiber is used as a propagation medium, fiber dispersion and nonlinear distortions effects appear. Dispersion in optical fiber is a linear effect that may be compensated by a dispersion compensating fiber. In contrast, the nonlinearity effect is one of the most unfavorable aspects of modern communication systems causing intermodulation distortion, adjacent channel interference, phase distortion, and harmonic distortion. In the majority of communication systems, the primary fiber nonlinear effect is the Kerr nonlinearity caused by the refractive index dependency on signal intensity. The purpose of this paper is to summarize a survey of fiber nonlinearity compensation techniques to minimize the effect of nonlinear distortion that improve the performance of optical communication network. The conclusions showed that there are two types of compensation, digital and optical. Optical compensation has better advantages than digital compensation in terms of efficient improving system performance and increasing data rate against nonlinear effects, especially for advanced systems with high capacity.