For nearly a century, ionizing radiation has been indispensable to medical diagnosis. Furthermore, various types of electromagnetic and particulate radiation have also been used in cancer therapy. However, the biological mechanism of radiation action remains incompletely understood. In this regard, a rapidly growing body of experimental evidence indicates that radiation exposure induces biological effects in cells whose nucleus has not been irradiated. This phenomenon termed the ‘non-targeted effects’ challenges the long-held tenet that radiation traversal through the cell nucleus is a prerequisite to elicit genetic damage and biological responses. The non-targeted effects include biological effects in cytoplasm-irradiated cells, bystander effects that arise in non-irradiated cells having received signals from irradiated cells, and genomic instability occurring in the progeny of irradiated cells. Such non-targeted responses are interrelated, and the bystander effect is further related with an adaptive response that manifests itself as the attenuated stressful biological effects of acute high-dose irradiation in cells that have been pre-exposed to low-dose or low-dose-rate radiation. This paper reviews the current body of knowledge about the bystander effect with emphasis on experimental approaches, in vitro and in vivo manifestations, radiation quality dependence, temporal and spatial dependence, proposed mechanisms, and clinical implications. Relations of bystander responses with the effects in cytoplasm-irradiated cells, genomic instability and adaptive response will also be briefly discussed.