This paper synthesizes and reviews progress in recent researches on the atmospheric dynamics in the stratosphere and its dynamical interaction with the tropospheric processes, with focuses on the dynamics of quasistationary planetary waves, the wave-basic flow interaction in the tropical stratosphere, the impact of atmospheric circulation variability in the stratosphere on circulation variability and climate in the troposphere, the numerical simulation of stratospheric atmosphere and climate projection in the stratosphere under the background of global warming. Recent researches revealed the waveguide variability of planetary waves and its association with northern annular mode, the importance of a wider spectrum of gravity waves in forcing a realistic quasi-biennial oscillation (QBO) and global meridional circulation, the cooling trend in the stratosphere and the importance of stratospheric processes for weather and climate anomalies near the surface. More in-depth studies on the atmospheric dynamics in the stratosphere and improvements of the model performance in the stratosphere will further promote the progress in the atmospheric science and climate change research.