Much is known about the biological effects of large doses of radiation but less is known about the effects of small doses. In most experiments with cells, plants and animals, large doses have been applied with clear and significant results. When the doses become smaller the effects decrease and become less clear. In order to compensate for this, the number of subjects (e.g., animals) can be increased. However, for the region where very small doses are involved (e.g., from an annual dose of a few mGy up to an acute dose of about 50 mGy), the number of animals or humans must be so large that it is very difficult (usually impossible) to conduct experiments and/or epidemiological studies. In epidemiological studies, attempts are made to correlate the radiation dose to the incidence of biological effects such as cancers in a large group of people. Some examples are the populations that have been exposed to radon, those exposed to the bombs at Hiroshima –Nagasaki, and those exposed during the Chernobyl accident. Such studies have yielded both conflicting and confusing results. They are, however, of considerable interest to scientists and to the public. In this chapter we will discuss known health effects and risks in the low dose region. We will concentrate on the incidence of cancer. The crucial factor is the dose-effect curve.