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Very long baseline interferometry offers the best means of investigating the complex dynamics of relativistic jets powered by active galactic nuclei, via multi-epoch, sub-milliarcsecond, full-polarization imaging at radio wavelengths. Although targeted studies have yielded important information on the structures of individual AGN jets, the strong selection effects associated with relativistically beaming imply that general aspects of the flows can only be determined via large statistical studies. In this review I discuss major results from the Monitoring of Jets in Active Galactic Nuclei With VLBA Experiments (MOJAVE) program, which has gathered multi-epoch Very Long Baseline Array (VLBA) data at 15 GHz on over 400 AGN jets over the course of two decades. The sample is large enough to encompass a range of AGN optical class, radio luminosity and synchrotron peak frequency, and has been used to show that within a particular jet, individual bright features have a spread of apparent speed and velocity vector position angle about a characteristic value. We have found that in some cases there is a secular evolution of launch angle direction over time, indicative of evolving narrow energized channels within a wider outflow. The majority of the jet features are superluminal and accelerating, with changes in speed more common than changes in direction. Within approximately 100 pc of the AGN, the flows are generally accelerating, while beyond this distance the flows begin to decelerate or remain nearly constant in speed. We also find evidence for a maximum bulk flow Lorentz factor of 50 in the pc-scale radio regime, and a trend of higher jet speeds in lower-synchrotron peaked and gamma-ray-loud blazars. Full article