Tumor-infiltrating leukocytes are often induced by the cancer microenvironment to display a protumor, proangiogenic phenotype. This "polarization" has been described for several myeloid cells, in particular macrophages. Natural killer (NK) cells represent another population of innate immune cells able to infiltrate tumors. The role of NK in tumor progression and angiogenesis has not yet been fully investigated. Several studies have shown that tumor-infiltrating NK (here referred to as "TINKs") and tumor-associated NK (altered peripheral NK cells, which here we call "TANKs") are compromised in their ability to lysew tumor cells. Recent data have suggested that they are potentially protumorigenic and can also acquire a proangiogenic phenotype. Here we review the properties of TINKs and TANKs and compare their activities to that of NK cells endowed with a physiological proangiogenic phenotype, in particular decidual NK cells. We speculate on the potential origins of TINKs and TANKs and on the immune signals involved in their differentiation and polarization. The TINK and TANK phenotype has broad implications in the immune response to tumors, ranging from a deficient control of cancer and cancer stem cells to an altered crosstalk with other relevant players of the immune response, such as dendritic cells, to induction of cancer angiogenesis. With this recently acquired knowledge that has not yet been put into perspective, we point out new potential avenues for therapeutic intervention involving NK cells as a target or an ally in oncology.