United Kingdom Meteorological Office global analyses from 1991 to 2001 are used to create a global climatology of stratospheric polar vortices and anticyclones. New methodologies are developed that identify vortices in terms of evolving three-dimensional (3-D) air masses. A case study illustrates the performance of the identification schemes during February and March of 1999 when a merger of anticyclones led to a stratospheric warming that split the Arctic polar vortex. The 3-D structure and temporal evolution of the Arctic vortex and identified anticyclones demonstrates the algorithm's ability to capture complicated phenomena. The mean geographical distribution of polar vortex and anticyclone frequency is shown for each season. The frequency distributions illustrate the climatological location and persistence of polar vortices and anticyclones. A counterpart to the Aleutian High is documented in the Southern Hemisphere: the Australian High. The temporal evolution of the area occupied by polar vortices and anticyclones in each hemisphere is shown as a function of potential temperature. Large polar vortex area leads to an increase in anticyclone area, which in turn results in a decrease in the size of the polar vortex. During Northern winter and Southern spring, 9 years of daily anticyclone movement are shown on the 1200 K (36 km, 4 hPa) isentropic surface. Preferred locations of anticyclogenesis are related to cross-equatorial flow and weak inertial stability. Regimes of traveling and stationary anticyclones are discussed.