A review is given of the theoretical and experimental situation concerning the problem of superconductivity in the presence of pair‐breaking perturbations. The problem was first considered by Abrikosov and Gorkov, who advanced a theory which explained the results of the experiments by Matthias and co‐workers on the lowering of Tc of superconductors containing small concentrations of magnetic impurities. The theory predicted further that the presence of magnetic scattering centers severely distorts the excitation spectrum of a superconductor and that for sufficiently large spin concentrations the energy gap disappears from the spectrum, even at T=0°K. It has since been found that the AG theory can be extended to treat other pair‐breaking situations which lead to second‐order superconducting‐normal phase transitions. Examples of these are the vortex state, the surface sheath state, the proximity effect, small superconductors in large magnetic fields, superconductivity in the presence of high currents, and superconductivity in the presence of strong Pauli paramagnetism. In the dirty limit (where the mean free path is much smaller than the zero‐temperature coherence length) the different pair‐breaking regimes are equivalent in that their behavior is specified by a unified single parameter theory. In transforming from one pair‐breaking regime to another, one needs only to change the pair‐breaking parameter. Experimental results from the different depairing regimes are presented and compared with the predictions of the unified theory.