•Epidemiological studies involving people exposed to low levels of ionizing radiation from the environment (natural and artificial sources), occupations or medical diagnostic procedures demonstrate that the risk of leukaemia and other cancers increases with radiation dose. •The latency between exposure to ionizing radiation and occurrence of an excess risk of cancer varies from several years to several decades. In addition, host factors such as age at exposure, attained age and sex modify the dose-risk relationship. •Most of the epidemiological research does not support an association between mobile phone use and tumours occurring in the head, the body part with the highest exposure to radiofrequency electromagnetic fields. Sporadic reports of associations are most likely false positive findings and the consequences of bias such as recall bias in retrospective exposure assessment.