Extrapolation of quantitative measurements across biological systems requires knowledge of field-organism interaction mechanisms. In the absence of such knowledge, one can only indicate which parameters would be important under some plausible assumptions that still lack experimental proof. In the first part of the paper it is assumed that biological effects of low intensity, extremely low frequency magnetic fields are caused by the electric fields which they induce. It is shown that detailed knowledge of electrical properties on a microscale is important to predict effects that may be due to local current density, electric field strength, surface charge distribution, and mechanical forces. In the second part of the paper, it is shown that all proposed mechanisms for direct interaction between alternating magnetic fields and cells involve also the magnitude and direction of a simultaneously present static magnetic field. Reviewed are "cyclotron resonance," quantum mechanical effects on ions weakly bound to proteins, nuclear magnetic resonance, and recent progress in magneto chemistry dealing with effects of magnetic fields of a few hundred microtesla on chemical reactions that involve free radicals.