A review is given of the dielectric properties of mammalian tissues for the frequency range 1 Hz to 10 GHz. Such information is of relevance to a number of medical diagnostic and therapeutic applications which involve the use of non-ionizing electromagnetic radiation, as well as to studies of the possible biological effects arising from exposure to electric and magnetic fields. Dielectric studies of tissues and biomolecules can also aid the further understanding of some biochemical and physiological processes. The dielectric properties of amino acids, proteins, biological electrolytes, cell membranes, tissue-bound water and of normal and cancerous tissues are discussed with the emphasis being directed at the underlying molecular and biophysical processes involved. Clinical aspects such as the hyperthermic treatment of cancer and the stimulation of bone healing are discussed also.