We report here on various biophysical aspects of irradiated cells, beginning with a phenomenological description of radiation-induced cancer cells. This description includes detrimental factors such as chromosomal aberrations, as well as beneficial factors, such as adaptive response. Also discussed here is the dose- and time-dependent evolution of cancer cells using a purely mathematical approach. The general dose-response shape, which is sigmoidal, is shown to be modified by such mechanisms as adaptive response or bystander effect. The many aspects of the sigmoid function, which most appropriately demonstrates the relationships among irradiated organisms, are discussed here as well. Finally, the balance equation is presented as the most general relationship for irradiated cell behavior.