This article describes the contributions of physics and radiobiology to the 'growing points' in the treatment of cancer by radiotherapy. Possible new methods of achieving better physical dose distributions in tissues and also improvements in diagnostic and prognostic tumour detection techniques are briefly discussed. The successes of using multiple-small-doses (hyperfractionation) of X-rays are reported; this is thought to be due to differing effects on the repair mechanism of tumour cells. The emphasis of the article is on the methods of overcoming the greater resistance to X-rays of hypoxic cells present in tumours. These include the use of hyperbaric oxygen, fast neutrons, negative pi mesons, heavy particle beams and hypoxic cell radiosensitizers. The effect of fractionation of X-rays, neutrons and radiosensitizers on tumour control are also discussed in relation to the effects on hypoxic cells subjected to hyperthermia following X-irradiation are reported. Combination treatments of radiotherapy and chemotherapy are briefly discussed. Finally, a summary of the estimates of the gain in cell kill in cancer treatment using various modalities is given; the elimination of hypoxic cells appears to be the largest effect, followed by hyperthermia.