There are two factors which will play the key roles in stratospheric climate changes in the 21st century. One is increasing greenhouse gases, and the other one is the likely recovery of stratospheric ozone. The radiative effect of increasing greenhouse gases causes warming on the surface and in the troposphere, but cooling in the stratosphere, whereas the recovery of the ozone layer will cause stratospheric warming. How stratospheric temperatures will be changed by the two opposite effects is the main interest in the present study. In order to explore changes in stratospheric temperatures, we carry out sensitivity simulations using a radiative-convective equilibrium model, and we also analyze simulation results from coupled chemistry-climate models (CCM). Our results show cooling trends in the middle and upper stratosphere (60~1 hPa) and warming in the lower layers (150～60 hPa). These suggest that the cooling effect of increasing greenhouse gases is more important in the middle and upper stratosphere, while the warming effect of ozone recovery plays the major role in the lower stratosphere. CCM simulations show that the maximum ozone increase is in the upper stratosphere (about 3 hPa), which matches the layer of maximum cooling trends, suggesting that increasing greenhouse gases will benefit stratospheric ozone recovery. CCM simulations also show warming trends in stratospheric polar regions in the winter half-year for both hemispheres. According to previous studies, the polar warming is due to increasing planetary wave activity in the stratosphere. In addition, feedbacks among dynamical, thermal and chemical processes may also contribute the polar warming.