The effect of ''strong'' electromagnetic fields on cells and tissue can be dramatic but not necessarily harmful. The essentially universal biophysical phenomenon of ''electroporation'' occurs if an applied field causes the cell transmembrane voltage to reach about 0.5--1 V in a time of microseconds to milliseconds. Ordinarily the cell membrane is a formidable barrier to the transport of ions and charged molecules. However, electroporation results in a large increase in transmembrane conductance, which is believed to be caused by ion transport through temporary membrane openings (''pores''). This high-conductance state limits the transmembrane voltage and thereby protects the membrane. A large increase in molecular transport generally occurs for the same conditions and allows polar molecules to be introduced into cells. Similar enhanced molecular transport can be caused in living tissues. Not only cell membranes, but also cell layers or even the stratum corneum of human skin can be temporarily altered by the electrical creation of aqueous pathways. The mechanism of electroporation is partially understood, in that the electrical and mechanical behavior of artificial planar bilayer membranes can be described quantitatively by a theoretical model based on transient aqueous pores. More complex behavior in cell membranes may be due to both the complicated shapes of cell membranes and the additional participation of metastable pores and interactions with cell structures. In the case of tissues the situation is even more complex and has only recently begun to be studied but has the prospect of providing a new approach to transporting polar molecules across tissue barriers. ¿ American Geophysical Union 1995