The advantages, high bandwidth and high speed, of optical Fourier transform have been proved to be highlighted since the frequency of the objective signal becomes increasingly complicated, further, it has significant applications in the fields of optical spectra and real-time detection of high-speed radio frequency signals. The optical Fourier transform based on fiber dispersion comprises two particular methods: dispersive pulse broadening and time lens. Based on the optical fiber dispersion method, the realization principles of optical Fourier transform based on dispersion broadening and time lens are compared and analyzed. In addition, it summarizes five representative approaches divided into two categories, analyzes the empirical performance including output, dispersion, spectral resolution, time-bandwidth product, and expounds the applicability and improvement of these approaches.