One of the most puzzling aspects of Mars is that organics have not yet been found on the surface. The simplest of organic molecules, methane, was detected in the Martian atmosphere for the first time in 2003. The existence and behavior of methane on Mars is of great significance, as methane is a potential biomarker. In this paper we review our current understanding of possible sources and sinks of methane on Mars. We also investigate the role of other trace species in the maintenance and removal of methane from the atmosphere, as well as of other organic material from the surface. In particular, we examine the exogenous, hydrogeochemical - especially serpentinization - and biological sources, for supplying methane to Mars. We suggest that comets and meteorites are the least likely, whereas low-temperature serpentinization is the most plausible of all candidates to explain the methane observations. Nevertheless, it is premature to rule out the role of biology in producing methane on Mars, in view of available data. It is important to note that the loss of methane to surface must also be factored into any "source" scenarios for methane. Ordinary heterogeneous loss process to surface tends to be very slow. On the other hand, a reactive surface could potentially accelerate the destruction of methane. If correct, it would imply that a larger source of methane is present than currently estimated on the basis of photochemical loss alone. A reactive surface can also explain why no organic material has ever been detected on the Martian surface. The surface could become reactive if some oxidizer were present. We suggest that vast quantities of a powerful oxidant, hydrogen peroxide, can be produced in electrochemistry triggered by electrostatic fields generated in the Martian dust devils and dust storms, and in normal saltation process close to the surface. Finally, current observations are inadequate to prove or disprove the existence of life on Mars, now or in the past. The question of extraterrestrial life is a fundamental one, and it should be addressed meticulously on future missions to Mars. Measurements planned on the Mars Science Laboratory (MSL), especially carbon isotopes and chirality, will go a long way in meeting this goal. A brief overview of the MSL Mission and measurements relevant to the question of life and habitability of Mars is also presented in this paper.