In response to anthropogenic forcing, climate models project tropical amplification of warming aloft and Arctic amplification of surface warming. The vertical and latitudinal structure of warming has important implications for the response of tropical and extratropical storms and the mean circulation to climate change. While previous studies have shown that key features of the tropical and polar warming response can be qualitatively understood from simple column models of temperature, namely Radiative-Convective Equilibrium (RCE) and Radiative-Advective Equilibrium (RAE) in the tropics and poles, we currently do not have a complete quantitative understanding of the spatio-temporal structure of RCE and RAE (energy balance regimes) and their connection to the vertical structure of warming (lapse rate regimes). Improving our understanding by linking theory and models of varying complexity increases our confidence in climate change projections, which exhibit structural and parameter uncertainty. In this thesis, I contribute to our understanding of Earth’s vertical and latitudinal temperature structure and its response to anthropogenic forcing. I use theory to define energy balance regimes and show that they provide a useful guide for the vertical warming response projected by state-of-the-art climate models. I use idealized models to show that surface heat capacity controls RCE in the midlatitudes and sea ice controls RAE in the polar regions in the modern climate. Quantitatively, however, the RCE warming response (moist adiabatic adjustment) overpredicts the amplification of tropical warming aloft. I quantify the contribution of mechanisms not included in the moist adiabat (surface heterogeneity, the direct CO2 effect, and convective entrainment) on this overprediction. Finally, I show a new energy balance regime emerges in the Arctic by the year 2100, coinciding with the emergence of convective activity, vanishing surface inversion, and melting sea ice. Together the results improve our understanding of and confidence in the warming response projected by comprehensive climate model projections.