It has been known for over 30 years how to calculate magnetic-flux-density and current-density profiles in the critical state of type-II superconducting slabs and cylinders subjected to parallel applied magnetic fields. These profiles, which are parameterized by the critical current density Jc, are dependent on magnetic history. Recent theoretical developments have now made it possible to easily calculate the critical-state magnetic-flux-density and current-density profiles associated with vortex penetration into thin superconducting strips and disks subjected to perpendicular applied magnetic fields and transport currents. In this paper we briefly review what has been done in Superconducting strips and disks, discuss the detailed behavior for a strip in an increasing applied perpendicular magnetic field, compare these results with those for a slab in an increasing parallel field, and finally present results for the measuring-circuit geometry dependence of the apparent hysteretic losses for a strip carrying an alternating current.