There is frequent debate in the media and the scientific published reports about the use of radiation for diagnosis and treatment, the benefits and risks of the nuclear industry, uranium mining and the storage of radioactive wastes. Driving this debate is increasing concern about reliance on fossil fuels for power generation for which alternatives are required. Unfortunately, there is generally a poor understanding of the relevant basic sciences compounded by widespread irrational fear of irradiation (radiation phobia). Radioactivity, with special reference to uranium and plutonium is simply described. How radiation affect tissues and the potential hazards to individuals and populations are explained. The origins of radiation phobia and its harmful consequences are examined. Whether we like it or not, Australia is heavily involved in the uranium industry by virtue of having one-third of the world's known reserves, exports of which are worth approximately $470m annually. As this paper has been written as simply as possible, it may also be of interest to readers who may have had little scientific training. It may be downloaded from the web using references provided in this article. It is concluded that ignorance and fear are major impediments to rational debate on radiation issues.