Referring to flow-visualization and laser-Doppler anemometer measurements of swirl and axial velocity profiles, we discuss the physics of the flow in a cylindrical vortex tube as various independent parameters are varied. Three main classes of flow occur, depending upon the location of a vortex jump within the vortex tube. We present evidence to suggest a connection between vortex breakdown and the criticality and stability of the vortex core upon which it occurs and attempt to reconcile the various explanations that have been proposed for the breakdown phenomenon. Similarities and differences between the present experiments and those of previous investigators are also pointed out. Finally, as an Appendix, we present the results of a hydraulic analogue of our vortex experiment.