Natural killer cells (NK cells) are traditionally attributed to the innate immune system. It is considered that previously received stimuli have little effect on the functioning of these immune cells. Indeed, NK cells even without prior sensitization provide a rapid effector response against tumor, virus-infected, or otherwise damaged cells. They have a limited repertoire of receptors, the expression of which does not require somatic recombination. However, recent data indicate that NK cells may acquire the properties specific to adaptive immune cells. In particular, NK cells have been shown to possess the features of immunological memory, namely, the ability to more quickly and effectively respond to a repeated stimulus. The mechanisms of memory acquisition in NK cells differ from those implemented in T and B lymphocytes and are still rather vague. Presumably, some of these mechanisms underlie the significant phenotypic and functional NK cell diversity emerging during their differentiation. The recent data accumulated in this area considerably change the existing immunology paradigm, which postulates a clear delineation of the adaptive and innate immune cells. The published data on phenotypic and functional characteristics of NK cells and particular changes in these characteristics during NK cell differentiation and generation of memory-like NK cells are reviewed.