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A critical review is presented of the currents and the electric and magnetic fields characteristic of each of the salient discharge processes which make up cloud-to-ground and intracloud lightning. Emphasis is placed on the more recent work in which measured waveform variation is in the microsecond and submicro- second range, since it is this time-scale that is of primary importance in lightning/aircraft interactions. The state of the art of the modeling of lightning currents and fields is discussed in detail. A comprehensive bibliography is given of all literature relating to both lightning measurements and models.