The Earth has warmed at an unprecedented pace in the decades of the 1980s and 1990s (IPCC in Climate change 2007: the scientific basis, Cambridge University Press, Cambridge, 2007). In Wu et al. (Proc Natl Acad Sci USA 104:14889-14894, 2007) we showed that the rapidity of the warming in the late twentieth century was a result of concurrence of a secular warming trend and the warming phase of a multidecadal (similar to 65-year period) oscillatory variation and we estimated the contribution of the former to be about 0.08A degrees C per decade since similar to 1980. Here we demonstrate the robustness of those results and discuss their physical links, considering in particular the shape of the secular trend and the spatial patterns associated with the secular trend and the multidecadal variability. The shape of the secular trend and rather globally-uniform spatial pattern associated with it are both suggestive of a response to the buildup of well-mixed greenhouse gases. In contrast, the multidecadal variability tends to be concentrated over the extratropical Northern Hemisphere and particularly over the North Atlantic, suggestive of a possible link to low frequency variations in the strength of the thermohaline circulation. Depending upon the assumed importance of the contributions of ocean dynamics and the time-varying aerosol emissions to the observed trends in global-mean surface temperature, we estimate that up to one third of the late twentieth century warming could have been a consequence of natural variability.