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The paper summarizes the theoretical basis for the RFP and reviews the status of research in this field. The RFP is a relaxed state system well described by Taylor's theory which explains many observations. The RFP is of interest because its study will increase the understanding of toroidal confinement in general, which might lead to better reactor designs, and the RFP itself has potential as a reactor, for example the improved, high energy density, compact RFP reactor. In the last five or ten years, RFP research has expanded, with some 15-20 machines operating or under construction, and the plasma parameters have improved substantially, with a confinement time of 0.5-1 ms and temperatures approaching 1 keV; values of βθ ∼ 5-15% are reached routinely. Following an overview of recent results, three key problems are discussed in more detail: (1) resistivity, edge physics and ion heating (the ions are heated by fluctuations which drive the RFP dynamo); (2) operation of the RFP with an (electrically) thin shell which permits the growth of new unstable modes which degrade the confinement; and (3) scaling. Over the current range of 0.5 MA, favourable scaling trends of temperature and confinement with current are identified, but experiments at much higher currents on the two mega-ampere machines – RFX at Padua and CPRF at Los Alamos – due to operate in the early 1990s, are needed. A brief account of the compact RFP reactor is given, followed by a summary with an indication of future trends.