We review the scientific literature since the 1960s to examine the evolution of modeling tools and observations that have advanced understanding of global stratospheric temperature changes. Observations show overall cooling of the stratosphere during the period for which they are available (since the late 1950s and late 1970s from radiosondes and satellites, respectively), interrupted by episodes of warming associated with volcanic eruptions, and superimposed on variations associated with the solar cycle. There has been little global mean temperature change since about 1995. The temporal and vertical structure of these variations are reasonably well explained bymodels that include changes in greenhouse gases, ozone, volcanic aerosols, and solar output, although there are significant uncertainties in the temperature observations and regarding the nature and influence of past changes in stratospheric water vapor. As a companion to a recent WIREs review of tropospheric temperature trends, this article identifies areas of commonality and contrast between the tropospheric and stratospheric trend literature. For example, the increased attention over time to radiosonde and satellite data quality has contributed to better characterization of uncertainty in observed trends both in the troposphere and in the lower stratosphere, and has highlighted the relative deficiency of attention to observations in the middle and upper stratosphere. In contrast to the relatively unchanging expectations of surface and tropospheric warming primarily induced by greenhouse gas increases, stratospheric temperature change expectations have arisen from experiments with a wider variety of model types, showingmore complex trend patterns associated with a greater diversity of forcing agents.