Demand for gas or liquid fuels has increased in recent decades, while environmental legislation strict to reduce environmental pollutants (especially sulfur compounds) from fuels. There are various methods to diminish sulfur compounds from gas or liquid fuels that adsorption method on solid sorbents has attracted the attention of many researchers because it is efficient, inexpensive and high-efficiency method. Articles studying and results of laboratory have shown that metal-organic framework structures due to unique properties such as high porosity and multiple pores, high surface area, higher adsorption, low energy compared to other adsorbents such as silica gel, zeolites, carbon and metal structures have shown higher performance in removing sulfur compounds from gas or liquid fuels. However, precise determination of their performance relative to other adsorbents depends on the operating conditions and the type of adsorbate. In spite of the differences in the experimental conditions, the sulfur capacities MOFs or their hybrids were significantly higher (0. 1 gS/g) the other adsorbents (0. 01gS/g) (more than 10 times). Although it should be noted that due to the differences of experimental condition, this comparison needs to be taken cautiously. These structures maintain their performance and stability after several adsorption-desorption cycles and have shown good results for sulfur removal. For this reason, these structures have been widely used as adsorbents for the removal of sulfur compounds from the gas or liquid phase, catalysts, sensors and etc.