Abundant supplies of oil form the foundation of modern industrial economies, but the capacity to maintain and grow global supply is attracting increasing concern. Some commentators forecast a peak in the near future and a subsequent terminal decline in global oil production, while others highlight the recent growth in ‘tight oil’ production and the scope for developing unconventional resources. There are disagreements over the size, cost and recoverability of different resources, the technical and economic potential of different technologies, the contribution of different factors to market trends and the economic implications of reduced supply. Few debates are more important, more contentious, more wide-ranging or more confused. This paper summarizes the main concepts, terms, issues and evidence that are necessary to understand the ‘peak oil’ debate. These include: the origin, nature and classification of oil resources; the trends in oil production and discoveries; the typical production profiles of oil fields, basins and producing regions; the mechanisms underlying those profiles; the extent of depletion of conventional oil; the risk of an approaching peak in global production; and the potential of various mitigation options. The aim is to introduce the subject to non-specialist readers.