Biophysical models for radon-related induction of lung cancer are developed with the aim of reducing the uncertainties in current risk estimates at low doses by a better understanding of the relevant mechanisms. These models can make use of the full dosimetric information when extracting information on, say, age-at-exposure, protraction or fractionation effects. It is found that irradiation by radon and its progeny does act on the initiating event of carcinogenesis (e.g. mutation), but its dominating effect is via promoting the division of already initiated cells. Data show that the concept of a unit of exposure giving, in an additive way, a unit of lung cancer risk is too limited, while relatively simple mechanistic assumptions described in this article do yield an adequate description of observations. Exposures in epidemiological data sets are measured with error. For various error models it has been shown that likelihood-based techniques of correction work reliably; likewise for biologically based cancer models. When several parameters are allowed to be exposure dependent, for example, initiation and promotion, then their relative importance is influenced.