This paper reviews the current understanding of low dose radiobiology, and how it has evolved from classical target theory. It highlights the uncertainty around low dose effects, which is due in part to the complexity of “context” surrounding the ultimate expression of biological effects following low dose exposure. The paper makes special reference to low dose non-targeted effects which, are currently ignored in radiation protection and population level risk assessment, because it is unclear what they mean for risk. The view of the authors is that this “lack of clarity” about what the effects mean is precisely the point. It indicates the uncertainty of outcomes after a given exposure. The uncertainty stems from multiple outcome options resulting from the intrinsic uncertainty of the stochastic interaction of low dose radiation with matter. This uncertainty should be embraced rather than eschewed. The impacts of the uncertainties identified in this paper is explored and an approach to quantifying mutation probability in relation to dose is presented.