Pyrite is separated from other minerals mainly by flotation. However, the hydrophilicity of pyrite is affected by many factors, causing it to easily enter the concentrate and consequently reduce the quality of concentrate. Highly efficient pyrite depressants can be selectively adsorbed on the surface of pyrite to improve its hydrophilicity, thereby increasing the flotation separation efficiency. Understanding the fundamental inhibition mechanism of depressants on pyrite is a prerequisite to improve the flotation desulfurization efficiency. The inhibition ability and mechanism of different types of pyrite depressants are reviewed in this manuscript. In recent years, molecular simulation has increasingly become a powerful tool to study the interaction between reagents and minerals, shedding new light on the adsorption mechanisms of reagents on mineral surfaces at the atomic and electronic levels. The properties of sulfide mineral and flotation reagents as well as the microscopic adsorption mechanistic studies of reagents on mineral surfaces based on quantum chemistry and molecular simulation are also reviewed.