A new data set of middle- and upper-stratospheric temperatures based on reprocessing of satellite radiances provides a view of stratospheric climate change during the period 1979-2005 that is strikingly different from that provided by earlier data sets. The new data call into question our understanding of observed stratospheric temperature trends and our ability to test simulations of the stratospheric response to emissions of greenhouse gases and ozone-depleting substances. Here we highlight the important issues raised by the new data and suggest how the climate science community can resolve them.