Nowadays, desulfurization of fuel oil has raised concern globally because of strict industrial and environmental legislations. Albeit hydrodesulfurization (HDS) has been extensively used in oil refineries to produce low sulfur oil (< 10 ppm) but not been proven as effective method for the removal of dibenzothiophene (DBT), benzothiophene (TH) and their derivatives. Subsequently, adsorptive desulfurization (ADS) and oxidative desulfurization (ODS) methods have been developed to achieve high removal efficiency. In the past decade, metal-organic frameworks (MOFs) and its composites as oxidative catalysts, as well as adsorbents, have attracted the researchers owing to high surface area, tunable properties, and reusable. The present review comprises use of MOFs and their composites for the removal of sulfur from fuel oil via ODS and ADS processes. Additionally, physicochemical properties of MOFs, mechanism, pros and cons of both process, regeneration, and future challenges have been discussed briefly. Moreover, current limitations and future prospective are also discussed.