We have a considerable amount of work ahead of us to determine the importance of the wealth of new information emerging in the fields of sub-cellular, cellular and tissue biology in order to improve the estimation of radiation risk at low dose and protracted dose-rate. In this paper, we suggest that there is a need to develop models of the specific health effects of interest (e.g., carcinogenesis in specific tissues), which embody as much of the mechanistic (i.e., biological) information as is deemed necessary. Although it is not realistic to expect that every radiation-induced process should or could be included, we can hope that the major factors that shape the time dependence of evolution of damage can be identified and quantified to the point where reasonable estimations of risk can be made. Regarding carcinogenesis in particular, the structure of the model itself plays a role in determining the relative importance of various processes. We use a specific form of a multi-stage carcinogenic model to illustrate this point. We show in a review of the application of this model to lung cancer incidence and mortality in two exposed populations that for both high- and low-LET radiation, there is evidence of an "inverse dose-rate" or protraction effect. This result could be of some considerable importance, because it would imply that risk from protracted exposure even to low-LET radiation might be greater than from acute exposure, an opinion not currently held in the radiation protection community. This model also allows prediction of the evolution of the risk over the lifetimes of the exposed individuals. One inference is that radiation-induced initiation (i.e., the first cellular carcinogenic event(s) occurring in normal tissue after the passage of the radiation) may not be the driving factor in the risk, but more important may be the effects of the radiation on already-initiated cells in the tissue. Although present throughout the length of the exposure, radiation-induced initiation appears to play a dominating role only very late in life, and only for those individuals who began their exposure early in life. These conclusions are very dependent, of course, on the hypotheses embodied in the initiation-promotion-conversion paradigm of carcinogenesis. We suggest that recently identified processes, such as the "bystander effect", might affect initiation, promotion, and malignant conversion in different ways. Finally, the manner in which the quality of radiation affects these processes must be understood in the context of the mixed high- and low-LET radiations that are found in the space environment. Important directions in critical experiment definition are suggested, including a renewed emphasis on well-designed animal experiments over extended periods of time.