A potential candidate material for the construction of Mars habitats is concrete made from the Martian regolith and sulfur extracted from the regolith itself. Sulfur concrete, which has excellent mechanical properties, can be prepared at a low temperature (<150 °) and without water (unlike Portland-cement concrete). The surface of Mars has a much higher concentration of sulfur than those of the Earth, the Moon, or the asteroids. Sulfur on Mars, however, exists not as elemental sulfur—which is needed in concrete production—but as sulfates (usually hydrated) and sulfides. This paper surveys thermochemical and electrochemical methods that might be used to produce elemental sulfur from its compounds contained in the minerals on Mars. Possible methods include chemical or electrochemical oxidation or decomposition of sulfides, which include sulfides that exist naturally on Mars as well as sulfides that are produced via chemical or electrochemical reduction of sulfates. Some of the methods to obtain elemental sulfur—such as chemical or electrochemical oxidation or decomposition of metal sulfides or hydrogen sulfide—have already been demonstrated. The methods of producing elemental sulfur from sulfur-containing minerals on Mars will have the added benefit of generating byproducts (e.g. water, hydrogen, oxygen, and metals) that are useful for explorations of the Red Planet. In the future, chemical processes for the production of elemental sulfur may also have important industrial applications on Earth.