It is widely accepted that damage to DNA is the critical event in irradiated cells, and that double strand breaks are the primary DNA lesions responsible for the biological effects of ionizing radiation. This has led to the long standing paradigm that these effects, be they cytotoxicity, mutagenesis or malignant transformation, occur in irradiated cells as a consequence of the DNA damage they incur. Evidence has been accumulating over the past decade, however, to indicate that radiation may induce effects that are not targeted to the irradiated cell itself. Two "'non-targeted effects will be described in this review. The first, radiation-induced genomic instability, is a phenomenon whereby signals are transmitted to the progeny of the irradiated cell over many generations, leading to the occurrence of genetic effects much a mutations and chromosomal aberrations arising in the distant descendants of the irradiated cell. Second, the bystander effect, is a phenomeon whereby irradiated cells transmit damage signals to non-irradiated cells in a mixed population, leading to genetic effects arising in these "bystander" cells that received no radiation exposure. The model system described in this review involves dense monolayer cultures exposed to very, low fluencess of alpha particles. The potential implications of these two phenomena for the analysis of the risk to the human population of exposure to low levels of ionizing radiation is discussed.