A hierarchy of models for type-II superconductors is presented. Through appropriate asymptotic limits the mesoscopic Ginzburg-Landau model is connected to the London model, to vortex-density models, and finally to macroscopic critical-state models such as the Bean model. The basic building block in deriving this hierarchy is the superconducting vortex which is a thin core of nonsuperconducting material circled by a superconducting electric current. Similar line singularities are found in other systems, for example, line vortices in an inviscid fluid, or Volterra dislocations in an elastic crystal. Analogous hierarchies for these systems are briefly discussed.