A review is given of the dielectric properties of various mammalian tissues and biological fluids for the frequency range from 1 Hz to 10 GHz. The properties considered are the frequency variations of the relative permittivity and electrical conductivity. An attempt has been made to present data which can be considered to be the most typical for each material. The dielectric properties of aqueous solutions of amino-acids, polypeptides, proteins, and then cells, are first outlined in order to lay the groundwork for the understanding of the properties of tissues. The electrical characteristics of various tissues and blood are presented in tabular and graphical form, and the differences between normal and cancerous tissue is also discussed. The effects of necrosis and temperature changes are described and the important contribution that water makes to the overall properties is emphasised. An insight into some of the dominant physiological and biophysical processes responsible for the dielectric properties of biological materials is also attempted, since this should aid further developments of both the diagnostic and therapeutic applications of radiofrequency and microwave radiation. Such information is also relevant to an understanding of the possible biological hazards of such radiation. The ways in which dielectric studies can aid an understanding at the molecular level of the basic physiological differences between normal and cancerous tissue, as well as of the physico-chemical state of biological water, are also described.