A special meeting of the Royal Society in London in 1986 marked the centenary of the first demonstration of nitrogen fixation. Currently the subject is of great practical importance because the use of nitrogenous fertilizers has resulted in unacceptable levels of water pollution; also these fertilizers are becoming steadily less economic both in cash terms and in utilization of fossil fuels for their manufacture. The number of papers published and the frequency of national and international meetings to discuss research into nitrogen fixation have both increased steadily during the 1970s and 1980s. Specialist monographs and review papers are often too detailed to be of real use to undergraduates in biology or related areas such as agriculture and forestry, and even for graduates and research workers newly entering the field of nitrogen fixation. For people in these categories, the senior author wrote The Biology of Nitrogen-fixing Organisms published by McGraw Hill in 1979. This book has similar aims. It incorporates new findings that have not only resolved some of the uncertainties reported in that earlier text hut, more importantly, it reflects the influence on the subject of recent developments in biochemistry, molecular biology, genetic engineering and other biotechnologies. We have devoted more attention to quantitative aspects of the subject, but unfortunately the many practical difficulties for accurate field assessment of nitrogen fixation and its contribution to nitrogen cycles means that many assessments are either in contlict with each other or must be accepted as tentative.