Recent observational and numerical modeling studies of the mechanisms which transport moisture to the stratosphere by deep convective storms at mid-latitudes are reviewed. Observational evidence of the cross-tropopause transport of moisture by thunderstorms includes satellite, aircraft and ground-based data. The primary satellite evidence is taken from both conventional satellite of thunderstorm images and CloudSat vertical cloud cross-section images. The conventional satellite images show cirrus plumes above the anvil tops of some of the convective storms where the anvils are already at the tropopause level. The CloudSat image shows an indication of penetration of cirrus plume into the stratosphere. The aircraft observations consist of earlier observations of the ¡§jumping cirrus¡¨ phenomenon reported by Fujita and recent detection of ice particles in the stratospheric air associated with deep convective storms. The ground-based observations are video camera records of the jumping cirrus phenomenon occurring at the top of thunderstorm cells. Numerical model studies of the penetrative deep convective storms were performed utilizing a three-dimensional cloud dynamical model to simulate a typical severe storm which occurred in the US Midwest region on 2 August 1981. Model results indicate two physical mechanisms that cause water to be injected into the stratosphere from the storm: (1) the jumping cirrus mechanism which is caused by the gravity wave breaking at the cloud top, and (2) an instability caused by turbulent mixing in the outer shell of the overshooting dome. Implications of the penetrative convection on global processes and a brief future outlook are discussed.