Natural killer (NK) cells are lymphocytes with a key role in the defense against viral infections and tumor cells. Although NK cells are classified as innate lymphoid cells (ILCs), under certain circumstances they exhibit adaptive and memory-like features. The latter may be achieved, among others, by a brief stimulation with interleukin (IL)-12, IL-15 and IL-18. These cytokine-induced memory-like (CIML) NK cells resemble the trained immunity observed in myeloid cells. CIML NK cells undergo transcriptional, epigenetic and metabolic reprogramming that, along with changes in the expression of cell surface receptors and components of cytotoxic granules, are responsible for their enhanced effector functions after a resting period. In addition, these memory-like NK cells persist for a long time, which make them a good candidate for cancer immunotherapy. Currently, several clinical trials are testing CIML NK cells infusions to treat tumors, mostly hematological malignancies. In relapse/refractory acute myeloid leukemia (AML), the adoptive transfer of CIML NK cells is safe and complete clinical remissions have been observed. In our review, we sought to summarize the current knowledge about the generation and molecular basis of NK cell memory-like responses and the up-to-date results from clinical trials with CIML NK cells.