Hematopoietic stem cells (HSCs) are a rare subset of bone marrow cells that usually exist in a quiescent state, only entering the cell cycle to replenish the blood compartment, thereby limiting the potential for errors in replication. Inflammatory signals that are released in response to environmental stressors, such as infection, trigger active cycling of HSCs. These inflammatory signals can also directly induce HSCs to release cytokines into the bone marrow environment, promoting myeloid differentiation. After stress myelopoiesis is triggered, HSCs require intracellular signaling programs to deactivate this response and return to steady state. Prolonged or excessive exposure to inflammatory cytokines, such as in prolonged infection or in chronic rheumatologic conditions, can lead to continued HSC cycling and eventual HSC loss. This promotes bone marrow failure, and can precipitate preleukemic states or leukemia through the acquisition of genetic and epigenetic changes in HSCs. This can occur through the initiation of clonal hematopoiesis, followed by the emergence preleukemic stem cells (pre-LSCs). In this review, we describe the roles of multiple inflammatory signaling pathways in the generation of pre-LSCs and in progression to myelodysplastic syndrome (MDS), myeloproliferative neoplasms, and acute myeloid leukemia (AML). In AML, activation of some inflammatory signaling pathways can promote the cycling and differentiation of LSCs, and this can be exploited therapeutically. We also discuss the therapeutic potential of modulating inflammatory signaling for the treatment of myeloid malignancies.