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While the annual mean Arctic Amplification (AA) index varied between two and three during the 1970–2000 period, it reached values exceeding four during the first two decades of the 21st century. The AA did not change in a continuous fashion but rather in two sharp increases around 1986 and 1999. During those steps the mean global surface air temperature trend remained almost constant, while the Arctic trend increased. Although the "best" CMIP6 models reproduce the increasing trend of the AA in 1980s they do not capture the sharply increasing trend of the AA after 1999 including its rapid step‐like increase. We propose that the first sharp AA increase around 1986 is due to external forcing, while the second step close to 1999 is due to internal climate variability, which models cannot reproduce in the observed time. Plain Language Summary: The rate of Arctic warming varied in time, while the rate of global warming was nearly constant over the period 1960–2020. This led to a variable Arctic Amplification (AA) defined as a ratio of the Arctic warming trend to mean global warming trend. In addition, the Arctic experienced sudden changes in the rate of warming with step‐like changes in annual mean Arctic Amplification around the years 1986 and 1999. Climate models do not capture the second observed sharp increase of the AA. We suggest that the first AA increase around 1986 is primarily due to external forcing (increasing concentration of carbon dioxide) while the second sharp increase around 1999 is dominated by internal climate variability which current models cannot capture accurately within the time scale of the physical phenomena. Key Points: Annual mean Arctic Amplification (AA) within the period 1970–2020 changed in steep steps around 1986 and 1999. It reached values over 4.0Even those CMIP6 models best at reproducing the AA did not reproduce the second sudden increase near 1999We conjecture that the first AA sharp increase is due to external forcing, while the second is due to internal climate variability [ABSTRACT FROM AUTHOR]