Epstein-Barr virus (EBV)-associated neoplasms derived from natural killer (NK) or T cells comprise a group of clinically and biologically heterogenous disorders affecting children and adults, which are overall rare but more prevalent in Asia and South America. This review focuses on neoplasms presenting in the adulthood, addressing recent genomic discoveries as well as therapeutic developments in these highly aggressive disorders. Distinct molecular subtypes of extranodal NK/T-cell lymphomas (ENKTCLs) have been described, with differences in cell of origin, EBV pattern, genomic alterations, clinical characteristics, response to asparaginase-based therapies and to more recent approaches targeting molecular aberrations of the lymphoma. For the last two decades, progress in the clinical management of ENKTCL was based on L-asapraginase containing combinations and the incoroperation of radiotherapy. A subset of cases with PDL1-2 structural alterations may be more responsive to treatment with immune checkpoint inhibitors. Primary nodal EBV+ lymphomas derived from T or NK cells have distinctive features separating them from both peripheral T-cell lymphoma not otherwise specified and ENKTCL. Treatment algorithms correspond to those for advanced ENKTCL. With better understanding of lymphomagenesis, genomic landscape and immunologic aspects of the diseases, future treatment options will include targeted therapies including immune checkpoint inhibitors and novel antibodies.