The alleged significant slowdown in global warming during the first decade of the 21st century, and the appearance of a discrepancy between models and observations, has attracted considerable research attention. We trace the history of this research and show how its conclusions were shaped by several sources of uncertainty and ambiguity about models and observations. As those sources of uncertainty were gradually eliminated by further research, there is now insufficient remaining evidence to infer any discrepancy between models and observations or a significant slowing of warming. We discuss possible reasons why the slowdown attracted so much public and research attention.