Previous studies have documented a poleward shift in the subsiding branches of Earth's Hadley circulation since 1979 but have disagreed on the causes of these observed changes and the ability of global climate models to capture them. This synthesis paper reexamines a number of contradictory claims in the past literature and finds that the tropical expansion indicated by modern reanalyses is within the bounds of models' historical simulations for the period 1979-2005. Earlier conclusions that models were underestimating the observed trends relied on defining the Hadley circulation using the mass streamfunction from older reanalyses. The recent observed tropical expansion has similar magnitudes in the annual mean in the Northern Hemisphere (NH) and Southern Hemisphere (SH), but models suggest that the factors driving the expansion differ between the hemispheres. In the SH, increasing greenhouse gases (GHGs) and stratospheric ozone depletion contributed to tropical expansion over the late twentieth century, and if GHGs continue increasing, the SH tropical edge is projected to shift further poleward over the twenty-first century, even as stratospheric ozone concentrations recover. In the NH, the contribution of GHGs to tropical expansion is much smaller and will remain difficult to detect in a background of large natural variability, even by the end of the twenty-first century. To explain similar recent tropical expansion rates in the two hemispheres, natural variability must be taken into account. Recent coupled atmosphere-ocean variability, including the Pacific decadal oscillation, has contributed to tropical expansion. However, in models forced with observed sea surface temperatures, tropical expansion rates still vary widely because of internal atmospheric variability.