Theories of vortex breakdown are constrained by the assumption of axial symmetry and steady flow. Neither assumption is approximated in aerodynamic vortices suffering breakdown. To what extent is it possible to infer information about the occurrence, location, and nature of a vortex breakdown event from the available theories? These questions are difficult to address by laboratory experiments. Numerical experiments can help, but the difficulties of numerical simulation in this problem are more severe than in many other fluid mechanical problems. The elements leading to the numerical difficulties are discussed. Questions posed about vortex breakdown are then revisited in the light of recent numerical experiments.