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We use a simple, semianalytic, column model to understand better the meridional structure of the tropopause height and future changes in its height and temperature associated with global warming. The model allows us to separate the effects of tropospheric lapse rate, optical depth, outgoing longwave radiation (OLR), and stratospheric cooling on the tropopause height. When applied locally at each latitudinal band, the model predicts the overall meridional structure of the tropopause height, with a tropical tropopause substantially higher than in higher latitudes and a sharp transition at the edge of the extratropics. The large optical depth of the Tropics, due mainly to the large water-vapour path, is the dominant tropospheric effect producing the higher tropical tropopause, whereas the larger tropical lapse rate actually acts to lower the tropopause height. The dynamical cooling induced by the stratospheric circulation lifts the thermal tropopause in the Tropics further, resulting in it being significantly cooler and higher than in mid- and high-latitudes. The model quantifies the causes of the tropopause height increase with global warming that is found robustly in climate integrations from the fifth Coupled Model Intercomparison Project (CMIP5). The large spread in the increase rate of tropopause height in the CMIP5 model is captured by the simple model, which attributes the dominant contributions to changes in water-vapour path and lapse rate, with changes in CO2 concentration and OLR having much smaller direct effects. The CMIP5 models also show a small but robust increase in the tropopause temperature in low latitudes, with a much smaller increase in higher latitudes. We suggest that the tropical increase may be caused at least in part by nongrey effects in the radiative transfer associated with the higher levels of water vapour in the Tropics, with near-constant tropopause temperatures predicted otherwise.