Human tissues conduct electricity about as well as semiconductors. However, there are large differences between tissues which have recently been shown to be determined mainly by the structure of the tissue. For example, the impedance spectrum of a layered tissue such as skin is very different to that of the underlying tissues. The way in which the cells are arranged and also the size of the nucleus are both important. Some of the recent developments in measurement and modelling techniques are described and the relationship between tissue structures and impedance spectra is outlined. The illustrations and examples look at the effect of premalignant changes on localised impedance spectra measured from cervical tissues. Electrical Impedance Tomographic measurements on lung tissue are used to show the maturational changes of lung structure in neonates. The conclusion contains some speculation as to what further research outcomes might occur over the next few years.