this paper presents a survey conducted on several digital signal processing techniques used to compensate for dispersion in optical fibers. DSP techniques have many advantages over other techniques such as the low cost associated with implementing DSP solutions and the reduced complexity. The techniques covered in this study include Finite Impulse Response (FIR), Savory's Method, All-Pass Filters, Least Mean Square Algorithm, Constant Modulus Algorithm, Fast Fourier Transform, Look-up Tables and Raised cosine filter. In addition to the survey, the paper also presents a MATLAB simulation based on constant modulus algorithm (CMA) to optimize an equalizer used to compensate dispersion. A constellation diagram was used to compare the signals before and after compensation. Results showed less scattered points in the constellation diagram after the equalizer, compared to the severely scattered one of the received signal before compensation. The effects of different number of filter taps are studied as well.