Polar amplification (PA), defined as the enhanced warming of the polar region relative to the global average, is a robust feature of historical observations and simulations of future climate. Because PA has yet to be realized in the Antarctic, I mainly focus on Arctic amplification (AA). Despite the far-reaching consequences of Arctic warming and sea ice loss, the causes of AA and their relative importance remain contested. This dissertation highlights some of the most important AA-producing mechanisms by analyzing the different timescales over which AA develops following an increase in CO₂ in climate model simulations. First, an Arctic and global average energy budget analysis is derived for a collection of Coupled Model Intercomparison Project version 5 (CMIP5) models subjected to an instantaneous quadrupling of CO₂ (4xCO₂). I quantify the relative contributions of various AA mechanisms using radiative kernels for 150 years after 4xCO₂ and compare mechanisms important at the beginning of the simulations against those when the models are in a quasi-equilibrium state. To focus on the fast timescales of AA, a new ensemble of Community Earth System Model (CESM) simulations was generated to observe the development of AA on ultrafast timescales (< 1 month) and to investigate the impact of the season in which CO₂ is increased. Finally, AA mechanisms and their seasonality are compared to those acting to produce Antarctic amplification (AnA). Motivated by this analysis, a new Python package called ClimKern was developed to simplify feedback calculations using radiative kernels and intercompare results based on different kernels. This work shows that AA occurs on incredibly fast timescales following CO₂ forcing, developing within three months in CMIP5 models and on the order of days in the CESM simulations in which CO₂ increases in January. The feedbacks important for AA immediately following CO₂ increase are not the same as those important decades afterward, demonstrating a strong time dependence of AA mechanism ...