Myeloid and lymphoid neoplasms with eosinophilia and abnormalities of PDGFRA, PDGFRB, or FGFR1 result from formation of a fusion gene encoding an aberrant tyrosine kinase. The cell of origin in those neoplasms associated with abnormalities of PDGFRA or FGFR1 is a mutated pluripotent (i.e., myeloid-lymphoid) stem cell, and thus the development of myeloid and lymphoid neoplasms associated with these abnormalities. Reported neoplasms associated with abnormalities of PDGFRB have been only myeloid in origin. This review presents the definitions and characteristic cytomorphological, immunophenotypic, cytogenetic, and molecular features of these neoplasms and discusses in depth the differential diagnoses. Following this presentation, the review then focuses on therapeutic approaches, including targeted therapy.