The advancements associated with modem day technology demands incorporation of the best physical understanding and the most accurate modelling of charged particle motion in gases. In recent times there have been major advances in the fundamental swarm transport theory, and this is the subject of the present paper. We start from 1986, when "multi-term" solutions of Boltzmann's equation for static electric fields had been developed to a sophisticated level, and proceed through to the present day, where the theory is motivated far more by application to industrial processes, which involve both electric and magnetic fields, either static or time varying. We present a unified time-dependent multi-term solution of Boltzmann's equation, emphasising the common methods and techniques underlying the treatment of all these situations, whether they be for electron or ion swarms. New and significant numerical results are presented to highlight the rich and diverse range of phenomena which are observed. (C) 2002 Elsevier Science B.V. All rights reserved.