If externally forced and internally generated climate variability interact on decadal timescales, it will most likely manifest as rapid shifts in warming. Here, the multi‐step bivariate test is applied to observed global and regional surface and satellite temperatures to determine the relative roles of shifts and trends. Statistically significant shifts dominate. Since the mid‐20th century, most of the observed warming has taken place in four events: in 1979/80 and 1997/98 at the global scale, 1987/88 in the northern hemisphere and 1968/70 in the southern hemisphere. Warming from internal trends is less than 40% of the total for four of five global records 1880–2013/14. Surface and tropospheric satellite temperature records (1979–2014), undergo similar step changes in 1987/88 and 1997, with limited internal trends between steps. Analyses for Texas, central England and south‐eastern Australia show step‐like warming that can be attributed to external forcing and coincides with these larger‐scale changes. Such evidence that the climate system is exhibiting complex system behaviour on decadal timescales is important information for characterising and managing future climate risk.