The transcription factor signal transducers and activators of transcription 5 (STAT5) has an important and unique role in Breakpoint Cluster Region - Abelson 1 (BCR-ABL1)-driven neoplasias. STAT5 is an essential component in the signaling network that maintains the survival and growth of chronic myeloid leukemia (CML) cells. In contrast, the function of the prototypical upstream kinase of STAT5, the Janus kinase JAK2, in CML is still under debate. Although there is widespread agreement that JAK2 is part of the signaling network downstream of BCR-ABL1, it is unclear whether and under what circumstances JAK2 inhibitors may be beneficial for CML patients. Recent studies in murine models have cast doubt on the importance of JAK2 in CML maintenance. Nevertheless, JAK2 has been proposed to have a central role in the cytokine signaling machinery that allows the survival of CML stem cells in the presence of BCR-ABL1 tyrosine kinase inhibitors. In this review, we summarize the current debate and provide an overview of the arguments on both sides of the fence. We present recent evidence showing that CML stem cells do not depend on BCR-ABL1 kinase activity but require the continuous support of the hematopoietic niche and its distinct cytokine environment and suggest that it has the potential to resolve the dispute.