Comparatively high exposures to power-frequency electric and magnetic fields produce established biological effects that are explained by accepted mechanisms and that form the basis of exposure guidelines. Lower exposures to magnetic fields (< 1 microT average in the home) are classified as "possibly carcinogenic" on the basis of epidemiological studies of childhood leukemia. This classification takes into consideration largely negative laboratory data. Lack of biophysical mechanisms operating at such low levels also argues against causality. We survey around 20 biophysical mechanisms that have been proposed to explain effects at such low levels, with particular emphasis on plausibility: the principle that to produce biological effects, a mechanism must produce a "signal" larger than the "noise" that exists naturally. Some of the mechanisms are impossible, and some require specific conditions for which there is limited or no evidence as to their existence in a way that would make them relevant to human exposure. Others are predicted to become plausible above some level of field. We conclude that effects below 5 microT are implausible. At about 50 microT, no specific mechanism has been identified, but the basic problem of implausibility is removed. Above about 500 microT, there are established or likely effects from accepted mechanisms. The absence of a plausible biophysical mechanism at lower fields cannot be taken as proof that health effects of environmental electric and magnetic fields are impossible. Nevertheless, it is a relevant consideration in assessing the overall evidence on these fields.