  We review recent developments in our understanding of how impurities
influence the electronic states in the bulk of superconductors. Our focus is on
the quasi-localized states in the vicinity of impurity sites in conventional
and unconventional superconductors and our goal is to provide a unified
framework for their description. The non-magnetic impurity resonances in
unconventional superconductors are directly related to the Yu-Shiba-Rusinov
states around magnetic impurities in conventional s-wave systems. We review the
physics behind these states, including quantum phase transition between
screened and unscreened impurity, and emphasize recent work on d-wave
superconductors. The bound states are most spectacularly seen in scanning
tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe
in detail. We also discuss very recent progress on the states coupled to
impurity sites which have their own dynamics, and impurity resonances in the
presence of an order competing with superconductivity. Last part of the review
is devoted to influence of local deviations of the impurity concentration from
its average value on the density of states in s-wave superconductors. We review
how these fluctuations affect the density of states and show that s-wave
superconductors are, strictly speaking, gapless in the presence of an
arbitrarily small concentration of magnetic impurities.
