Everyone is exposed to radiation from natural, man-made and medical sources, and world-wide average annual exposure can be set at about 3.5 mSv. Exposure to natural sources is characterised by very large fluctuations, not excluding a range covering two orders of magnitude. Millions of inhabitants are continuously exposed to external doses as high as 10 mSv per year, delivered at low dose rates, very few workers are exposed above the legal limit of 50 mSv/year, and referring to accidental exposures, only 5% of the 116,000 people evacuated following the Chernobyl disaster encountered doses above 100 mSv. Epidemiological survey of accidentally, occupationally or medically exposed groups have revealed radio-induced cancers, mostly following high dose-rate exposure levels, only above 100 mSv. Risk coefficients were derived from these studies and projected into linear models of risk (linear non-threshold hypothesis: LNT), for the purpose of risk management following exposures at low doses and low dose-rates. The legitimacy of this approach has been questioned, by the Academy of sciences and the Academy of medicine in France, arguing: that LNT was not supported by Hiroshima and Nagasaki studies when neutron dose was revisited; that linear modelling failed to explain why so many site-related cancers were obviously non-linearly related to the dose, and especially when theory predicted they ought to be; that no evidence could be found of radio-induced cancers related to natural exposures or to low exposures at the work place; and that no evidence of genetic disease could be shown from any of the exposed groups. Arguments were provided from cellular and molecular biology helping to solve this issue, all resulting in dismissing the LNT hypothesis. These arguments included: different mechanisms of DNA repair at high and low dose rate; influence of inducible stress responses modifying mutagenesis and lethality; bystander effects allowing it to be considered that individual cellular responses reflected in fact the results of multiple cellular interactions. Following the conclusion of the French Academy of medicine, LNT modelling resulted in public anxiety by changing an hypothetical residual risk at low doses into a real one, calling on regulators, continuously, for a more and more severe control of tiny sources which may result in considerable collective doses when considered as being exposed to billions of people for hundreds of years. Examples were provided that showed that the perception of risk of radioactive sources was not related to the severity of the risk itself but to the importance attributed to the situation by the media. In some instances, such as those resulting from the loss of gammagraphy sources, it resulted in a dangerous underestimate of the necessary remedial actions.