NK cells are cytotoxic components of innate lymphoid cells (ILC) that provide a first line of defense against viral infections and contribute to control tumor growth and metastasis. Their function is finely regulated by an array of HLA-specific and non-HLA-specific inhibitory and activating receptors which allow to discriminate between healthy and altered cells. Human NK cells gained a major attention in recent years because of the important progresses in understanding their biology and of some promising data in tumor therapy. In this review, we will outline well-established issues of human NK cells and discuss some of the open questions, debates, and recent advances regarding their origin, differentiation, and tissue distribution. Newly defined NK cell specializations, including the impact of inhibitory checkpoints on their function, their crosstalk with other cell types, and the remarkable adaptive features acquired in response to certain virus infections will also be discussed.