A survey is done on the effects of impurities in different types of superconductors, both conventional and unconventional, on their electronic spectra and physical properties. These effects can be generally divided on the base of validity (or not) for them of the known Anderson theorem, which is determined by the symmetries of the superconducting state vs those of the impurity perturbation. In this regard, the unconventional behavior can be naturally attributed to this theorem's failure when the impurity effects are generally much stronger and more diverse. Specific forms of such perturbations in different superconducting systems are analyzed and they reveal a variety of possible scenarios for quasiparticle spectra modification, including formation of several superconducting phases, distinguished by the types of specific narrow bands within the main spectrum gap. These phases and transitions between them, including the transition to the normal metal state, present a lot of unconventional features that can be of interest for some practical applications. The concluded observable effects are compared to the available experimental data.

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