In the past four decades much has been discovered about tornado formation and structure from observations, laboratory models, and numerical-simulation experiments. Observations include nearby movies and photographs of tornadoes, fixed-site, airborne, and ground-based mobile Doppler radar remote measurements, and in situ measurements using instrumented probes. Laboratory models are vortex chambers and numerical-simulations are based on the governing fluid dynamical equations. However, questions remain: How and why do tornadoes form? and How does the wind field associated with them vary in space and time? Recent studies of tornadoes based on observations, particularly by radar, are detailed. The major aspects of numerically simulating a tornado and its formation are reviewed, and the dynamics of tornado formation and structure based on both observations and laboratory and numerical-simulation experiments are described. Finally, future avenues of research and suggested instrument development for furthering our knowledge are discussed.