Various theoretical models of blinking fluorescence from a single semiconductor core-shell nanocrystal (NC) are discussed from the standpoint of consistency with new experimental data, with most of the emphasis placed on the charging model and the multiple recombination center model. The advantages and disadvantages of each are analyzed, and their recently proposed combination using the advantages of both is examined, which is capable of describing the recently observed properties of A- and B-type NCs (the two types differ by whether the fluorescence quantum yield of a single NC correlates with its fluorescence lifetime). It is shown that the Auger neutralization of the NC core results in an anticorrelation of the off-interval duration and the grey emission lifetime in the off interval. It is also shown that the exponent in the tin power-law distribution of on- and off-intervals in the fluorescence of single NCs characterizes the concentration of traps and localized NC core excitations at the core-shell interface.