The use of ionising radiations is so well established, especially in the practice of medicine, that it is impossible to imagine contemporary life without them. At the same time, ionising radiations are a known and proven human carcinogen. Exposure to radiation in some contexts elicits fear and alarm (nuclear power for example) while in other situations, until recently at least, it was accepted with alacrity (diagnostic x-rays for example). This non-uniform reaction to the potential hazards of radiation highlights the importance of quantitative risk estimates, which are necessary to help put things into perspective. Three areas will be discussed where quantitative risk estimates are needed and where uncertainties and limitations are a problem. First, the question of diagnostic x-rays. CT usage over the past quarter of a century has increased about 12 fold in the UK and more than 20 fold in the US. In both countries, more than 90% of the collective population dose from diagnostic x-rays comes from the few high dose procedures, such as interventional radiology, CT scans, lumbar spine x-rays and barium enemas. These all involve doses close to the lower limit at which there are credible epidemiological data for an excess cancer incidence. This is a critical question; what is the lowest dose at which there is good evidence of an elevated cancer incidence? Without low dose risk estimates the risk-benefit ratio of diagnostic procedures cannot be assessed. Second, the use of new techniques in radiation oncology. IMRT is widely used to obtain a more conformal dose distribution, particularly in children. It results in a larger total body dose, due to an increased number of monitor units and to the application of more radiation fields. The Linacs used today were not designed for IMRT and are based on leakage standards that were decided decades ago. It will be difficult and costly to reduce leakage from treatment machines, and a necessary first step is to refine the available radiation risks at the fractionated high doses characteristic of radiotherapy. The dose response for carcinogenesis is known for single doses up to about 2 Sv from the A-bomb data, but the shape at higher fractionated doses is uncertain. Third, the proliferation of proton facilities. The improved dose distribution made possible by charged particle beams has created great interest and led to the design and building of many expensive proton centres. However, due to technical problems, most facilities use passive scattering, rather than spot scanning, to spread the pencil beam to cover realistic target volumes. This process, together with the methods used of final collimation, results in substantial total body doses of neutrons. The relative biological effectiveness of these neutrons is not well known, and the risk estimates are therefore uncertain. Unless and until the risks are known with more certainty, it is difficult to know how much effort and cost should be directed towards reducing, or eliminating, the neutron doses. These three examples, where uncertainties in quantitative risk estimates result in important practical problems, will be discussed.