People are more often exposed to low as opposed to high doses of ionising radiation (IR). Knowledge on the health risks associated with exposures to ionising radiation above 100 mGy is quite well established, while lower dose risks are inferred from higher level exposure information (ICRP). The health risk assessments are mainly based on epidemiological data derived from the atomic bombing of Hiroshima and Nagasaki, medical exposure studies and follow-up studies after nuclear accidents. For the estimation of long-term stochastic radiation health effects (such as cancer) and radiation protection purposes, a linear non-threshold (LNT) model is applied. However, the general validity of the LNT hypothesis for extrapolations from effects of high to low doses (<100 mGy) and low dose-rates (<6 mGy/h) has been questioned as epidemiological studies are statistically limited at low doses and unable to evaluate low dose and low dose-rate health risks (UNSCEAR). Thus, uncertainties on health risks need to be clarified with the help of mechanistic studies. The European Network of Excellence DoReMi (2010-2016) was designed to address some of the existing uncertainties and to identify research lines that are likely to be most informative for low dose risk assessment. The present review reports the results obtained from studies addressing the induction of cancer and non-cancer effects by low dose IR as well as on individual radiation sensitivity. It is shown that low dose and low dose-rate effects are the result of complex network responses including genetic, epigenetic, metabolic and immunological regulation. Evidence is provided for the existence of nonlinear biological responses in the low and medium dose range as well as effects other than the classical DNA damage. Such effects may have a bearing on the quantitative and qualitative judgements on health effects induced by low dose radiations.