Radon-222, an inert and radioactive gas stemming from the uranium decay series, and its progeny are often used as tracers to study transfers in soils and in the atmosphere. They have also been studied on the surface of the Moon in connection with lunar outgassing. On Mars, where radon has never been studied nor measured so far, we show that their measurement could provide new insight and constraints on the chemical nature of the hydrogen measured in the Martian soil, in surface-atmosphere exchange processes, in atmospheric transport and, finally, in the dust cycle. Our approach is based on a coupled soil-atmosphere transport model implemented into the Global Circulation Model LMDZ. It includes the source term, the diffusion and adsorption of radon within the soil, and its atmospheric transport. The model input parameters are derived either experimentally (emanation factor and adsorption coefficient extrapolated to low temperatures) or by realistic models of porous media (diffusion coefficient at low pressure and as a function of the water saturation level). The model yields predictive maps of the radon exhalation rate as well as 3D fields of concentration in the soil and atmosphere, which will allow direct comparison with bismuth-214 measurements made by the GRS onboard the Mars Odyssey orbiter. We present preliminary results on this subject. An analysis of alpha spectra acquired by the APXS of the rover Opportunity is also presented, which shows evidence of a polonium-210 deposit on atmospheric dust, providing the first indirect proof of the presence of radon in the Martian atmosphere. We propose a simplified dust cycle model that enables us to infer an estimate of the global average radon exhalation rate on Mars. Lastly, we simulate the performance of an alpha spectrometer aimed at measuring radon and its progeny on the surface of the planet.