There is a growing research interest in understanding extreme weather in the context of anthropogenic climate change, posing a requirement for new tailored climate data products. Here we introduce the Climate of the 20th Century Plus Detection and Attribution project (C20C + D&A), an international collaboration generating a product specifically intended for diagnosing causes of changes in extreme weather and for understanding uncertainties in that diagnosis. The project runs multiple dynamical models of the atmosphere-land system under observed historical conditions as well as under naturalised versions of those observed conditions, with the latter representing how the climate system might have evolved in the absence of anthropogenic interference. Each model generates large ensembles of simulations with different initial conditions for each historical scenario, providing a large sample size for understanding interannual variability, long-term trends, and the anthropogenic role in rare types of weather. This paper describes the C20C + D&A project design, implementation, strengths, and limitations, and also discusses various activities such as this special issue of Weather and Climate Extremes dedicated to "First results of the C20C + Detection and Attribution project".