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British psychologists have been at the forefront of research into human reasoning for 40 years. This article describes some past research milestones within this tradition before outlining the major theoretical positions developed in the UK. Most British reasoning researchers have contributed to one or more of these positions. We identify a common theme that is emerging in all these approaches, that is, the problem of explaining how prior general knowledge affects reasoning. In our concluding comments we outline the challenges for future research posed by this problem.