The MARS code system is a set of Monte Carlo programs for detailed simulation of hadronic and electromagnetic cascades in an arbitrary geometry of shielding, accelerator, detector and spacecraft components with energy ranging from 10^-5 electronvolt up to 100 TeV. It was originated in 1974 at MEPhI (Moscow), and developed since at IHEP (Protvino), SSCL (Texas) and Fermilab. Current MARS15 combines well established theoretical models for strong, weak and electromagnetic interactions of hadrons, heavy ions and leptons with a system which can contain millions of objects, ranging in dimensions from microns to hundreds of kilometers in the same setup. MARS is especially powerful in accelerator, beamline and machine-detector interface applications including but not limited to radiation protection, shielding design, environment control, radiation damage, and materials research. The code was used in design of accelerator systems at U-70, UNK, Tevatron, Main Injector, Booster, SSC, LHC, NLC, TESLA, ILC, KEK, J-PARC, ESS and muon colliders: beam abort, beam stops, scrapers, collimators, beam transfer lines, beam loss monitors, interaction regions, target stations, and pioneering scheme of protection of superconducting magnets against deleterious radiation effects. Another class of MARS use is design of various detector and experimental setup components: experiments at U-70 and UNK at IHEP; D0, CDF, BTeV, E-853, T-864, E-872, NuMI/MINOS, Mu2e, LBNF, g-2 and SeaQuest at Fermilab; SFT, EMPACT, GEM, SDC and FAD at SSC; CMS at LHC as well as detectors for electron and muon colliders.