Arctic variability is dominated by multi-decadal fluctuations. Incomplete sampling of these fluctuations results in highly variable arctic surface-air temperature (SAT) trends. Modulated by multi-decadal variability, SAT trends are often amplified relative to northern-hemispheric trends, but over the 125-year record we identify periods when arctic SAT trends were smaller or of opposite sign than northern-hemispheric trends. Arctic and northern-hemispheric air-temperature trends during the 20th century (when multi-decadal variablity had little net effect on computed trends) are similar, and do not support the predicted polar amplification of global warming. The possible moderating role of sea ice cannot be conclusively identified with existing data. If long-term trends are accepted as a valid measure of climate change, then the SAT and ice data do not support the proposed polar amplification of global warming. Intrinsic arctic variability obscures long-term changes, limiting our ability to identify complex feedbacks in the arctic climate system.