In 1976, the Viking landers carried out the most comprehensive search for organics and microbial life in the martian regolith. Their results indicate that Mars' surface is lifeless and, surprisingly, depleted in organics at part-per-billion levels. Several biology experiments on the Viking landers gave controversial results that have since been explained by the presence of oxidizing agents on the surface of Mars. These oxidants may degrade abiotic or biological organics, resulting in their nondetection in the regolith. As several exploration missions currently focus on the detection of organics on Mars (or will do so in the near future), knowledge of the oxidative state of the surface is fundamental. It will allow for determination of the capability of organics to survive on a geological timescale, the most favorable places to seek them, and the best methods to process the samples collected at the surface. With this aim, we review the main oxidants assumed to be present on Mars, their possible formation pathways, and those laboratory studies in which their reactivity with organics under Mars-like conditions has been evaluated. Among the oxidants assumed to be present on Mars, only four have been detected so far: perchlorate ions (ClO₄^-) in salts, hydrogen peroxide (H₂O₂) in the atmosphere, and clays and metal oxides composing surface minerals. Clays have been suggested as catalysts for the oxidation of organics but are treated as oxidants in the following to keep the structure of this article straightforward. This work provides an insight into the oxidizing potential of the surface of Mars and an estimate of the stability of organic matter in an oxidizing environment.