This review focuses on topical issues in the biology and treatment of the myeloproliferative neoplasms (MPNs). Studies in transgenic mice suggest that BCR-ABL1 reduces the fraction of self-renewing 'leukemic' stem cells in the bone marrow but that some of these cells survive treatment with imatinib. This also seems to operate in humans. Data from models also strongly support the notion that JAK2(V617F) can initiate and sustain MPNs in mice; relevance to disease in humans is less clear. These data also support the hypothesis that level of JAK2(V617F) expression influences the MPN phenotype: higher levels favor erythrocytosis whereas lower levels favor thrombocytosis. Although TET2-mutations were thought to precede JAK2(V617F) in some persons with MPNs, it now appears that TET2 mutations may occur after JAK2(V617F). Further understanding of signal-transduction pathways activated in chronic myeloid leukemia suggests various possible targets for new therapies including the WNT/beta catenin, notch and hedgehog pathways. Finally, the clinical role of the new JAK2- and BCR-ABL1-inhibitors is considered. Much further progress is likely in several of these areas soon.