The market for biogas production has been increasing every year all over the world. The use of biogas as an energy vector is accomplished through the most diverse applications, such as direct burning (thermal energy), internal combustion engines, and fuel cells. Besides direct applications, biogas can be used as a raw material for producing high added-value products, such as molecular hydrogen and renewable hydrocarbons, through a new enterprise concept, the biorefineries. Purity and quality control are determinant factors that enable the decision-making regarding the end use of biogas. Physical, chemical, and biological methods can be used in biogas upgrading processes as well as a combination of different techniques. This review aims to deepen the knowledge about relevant technologies for biogas purification. It also addresses the most efficient and feasible methods, challenges to be overcome, and main demands for future studies. Therefore, the presentation, in a detailed way, of the synergistic effects caused by components contained in natural biogas and the combinatorial methods for removing these contaminants, differentiates this from other works that approach only the purification techniques but do not point out their problems and causes more comprehensively. Thus, studies related to the combined effects of contaminants would be interesting in future works.