Our understanding of mature aggressive B cell lymphomas has evolved significantly in the last years as reflected in the 2016 update of the WHO lymphoma classification. A main topic of the 2016 European Association for Haematopathology/Society of Hematopathology lymphoma workshop in Basel therefore was the clinicopathological spectrum of mature aggressive B cell lymphomas with the exception of conventional diffuse large B cell lymphoma. In this review, we summarize two sessions dedicated to "high-grade B cell lymphomas, with MYC and BCL2 and/or BCL6 rearrangements (so-called double/triple-hit lymphomas)" and "high-grade B cell lymphomas, NOS" as defined in the 2016 update of the WHO lymphoma classification, Burkitt lymphoma and related neoplasms, and terminally differentiated aggressive B cell lymphomas. One focus was on cases of Burkitt lymphoma with unusual clinical features such as spontaneous regression or association with immunosuppression, and the new provisional category of Burkitt-like lymphoma with 11q aberration. The large numbers of cases submitted for the new high-grade categories with or without genetic "double/triple hit" demonstrated the broad clinical and pathological spectrum of this group and gave ample opportunity for discussion. In this review, current definitions and our understanding of the main high-grade categories, potential problem areas, and suggestions for the immunophenotypic and genetic work-up of these neoplasms are discussed and illustrated by many interesting and challenging cases submitted to the workshop.