Non-sulfide, sulfur-rich minerals, dominated by sulfates, are particularly common in sedimentary rocks and other surficial environments, including those of anthropological origin (e.g., mine tailings), on both Earth and Mars. They vary significantly in the fundamental building block necessary for their formation ranging from the conventional sulfate [SO4]2− group to the less common bisulfate [HSO4]−, fluorosulfate [SO3F]−, thiosulfate [SO3S]2−, and methanesulfonate [SO3(CH3)]− as well as mixed anion groups. Other non-sulfide sulfur-rich minerals, such as sulfites and thiocyanates of the [SO3]2− and [SCN]− anion groups, respectively, are rare. Unlike their silicate, borate, and phosphate counterparts, the most salient feature of sulfate minerals is that the sulfate [SO4]2− group does not polymerize under any of the P–T conditions investigated to date. However, the linkages between the sulfate [SO4]2− group and metal polyhedra in sulfate minerals are complex and diverse. For example, the CuXn polyhedra (where X = O, OH, H2O, Cl, and n = 4–6) in Cu sulfate minerals can link to form diverse polyhedral configurations by sharing corners or edges with the [SO4]2− group in complex monodentate or bidentate modes, resulting in distinct magnetic properties. Numerous experimental and theoretical studies have investigated the effects of pressure and temperature on the stability and crystal structures of sulfate minerals, especially those of hydrous sulfate minerals. Sulfate minerals exert important controls on the fate of many heavy metals, metalloids, and radionuclides in the environment and have wide economic applications as cultural and industrial materials. In addition, some rock-forming minerals such as apatites, cancrinites, scapolites, and sodalities can contain elevated sulfur contents of variable speciation from the oxidized sulfate and sulfite groups to reduced sulfide and polysulfide species, representing excellent proxies for constraining redox states. For example, sulfur speciation in apatites has been calibrated as an oxybarometer with diverse applications from understanding magmatic-hydrothermal processes and associated mineralization to paleoclimatic reconstruction and planetary evolution. However, most rock-forming minerals contain only trace amounts of sulfur below the detection limits of the latest electron microprobe technology, making its speciation characterization challenging and often requiring the application of multiple advanced analytical techniques such as electron paramagnetic resonance spectroscopy, synchrotron X-ray absorption spectroscopy, and synchrotron X-ray emission spectroscopy.