Observations of the Martian surface from orbiting spacecraft and in situ landers and rovers, as well as analyses of Martian meteorites in terrestrial laboratories, have consistently indicated that Mars is a sulfur-rich planet. The global inventory of sulfur, from the atmosphere to the core, carries widespread implications of potential geophysical, geochemical, climatological, and astrobiological significance. For example, the sulfur content of the core carries implications for core density; the speciation of igneous sulfur minerals reflects the oxidation state of the magma from which they formed; sulfur-bearing gases may have exerted control on the temperatures at the surface of early Mars; and the widespread availability of sulfur on Mars would have provided an abundant source for energy and nutrients to fuel sulfur-metabolizing microbes, such as those that arose during the emergence of primitive life on Earth. Here we provide an overview of Martian sulfur and its relevance to these areas of interest, including a discussion of analytical techniques and results acquired by space missions and meteorite analyses to date. We review current studies modeling the potential effects of sulfur-bearing gases on the past Martian climate and possible constraints on atmospheric composition implied by sulfur isotopic data. We also explore the importance of sulfur to the search for extinct or extant life on Mars. Finally, we summarize a few areas of interest to future work, including advances in space exploration technology and preparation for Mars sample return.