Basophils form a distinct cell lineage within the hematopoietic cell family. In various myeloid neoplasms, including chronic myeloid leukemia, basophilia is frequently seen. Acute and chronic basophilic leukemias, albeit rare, have also been described. However, no generally accepted criteria and classification of basophilic leukemias have been presented to date. To address this unmet need, a series of Working Conferences and other meetings were organized between March 2015 and March 2016. The current article provides a summary of consensus statements from these meetings, together with proposed criteria to delineate acute basophilic leukemia (ABL) from chronic basophilic leukemia (CBL) and primary forms of the disease where no preceding myeloid malignancy is detected, from the more common 'secondary' variants. Moreover, the term hyperbasophilia (HB) is proposed for cases with a persistent peripheral basophil count ⩾1000 per μl of blood. This condition, HB, is highly indicative of the presence of an underlying myeloid neoplasm. Therefore, HB is an important checkpoint in the diagnostic algorithm and requires a detailed hematologic investigation. In these patients, an underlying myeloid malignancy is often found and is then labeled with the appendix -baso, whereas primary cases of ABL or CBL are very rare. The criteria and classification proposed in this article should facilitate the diagnosis and management of patients with unexplained basophilia and basophil neoplasms in routine practice, and in clinical studies.