Aberrant Janus kinase-signal transducer and activator of transcription (JAK-STAT) signaling is implicated in the pathogenesis of acute myeloid leukemia (AML), a highly heterogeneous hematopoietic malignancy. The management of AML is complex and despite impressive efforts into better understanding its underlying molecular mechanisms, survival rates in the elderly have not shown a substantial improvement over the past decades. This is particularly due to the heterogeneity of AML and the need for personalized approaches. Due to the crucial role of the deregulated JAK-STAT signaling in AML, selective targeting of the JAK-STAT pathway, particularly constitutively activated STAT3 and STAT5 and their associated upstream JAKs, is of great interest. This strategy has shown promising results in vitro and in vivo with several compounds having reached clinical trials. Here, we summarize recent FDA approvals and current potential clinically relevant inhibitors for AML patients targeting JAK and STAT proteins. This review underlines the need for detailed cytogenetic analysis and additional assessment of JAK-STAT pathway activation. It highlights the ongoing development of new JAK-STAT inhibitors with better disease specificity, which opens up new avenues for improved disease management.