Acute myeloid leukemia (AML) remains a highly heterogeneous hematologic malignancy in which therapeutic resistance and disease relapse are largely driven by leukemic stem cells (LSCs). These rare, self-renewing cells possess unique biological properties that enable them to survive conventional chemotherapy and targeted therapies, thereby sustaining minimal residual disease and promoting leukemia re-emergence. LSC persistence arises from a complex and multilayered network of resistance mechanisms, including intrinsic cellular programs, adaptive molecular plasticity, and protective interactions within the bone marrow microenvironment. Intrinsic mechanisms include cellular quiescence, enhanced multidrug efflux activity, resistance to apoptosis and senescence, and activation of stress-adaptive pathways such as autophagy. In addition, LSCs exhibit remarkable metabolic and epigenetic flexibility, allowing them to rewire signaling pathways and survive therapeutic pressure. Extrinsic cues from the bone marrow niche, including stromal interactions, cytokine signaling, and metabolic support, further reinforce the survival and drug tolerance of LSCs. Together, these interconnected mechanisms create a highly resilient cellular state that limits the efficacy of current therapies. In this review, we summarize the major biological pathways that sustain LSC-mediated resistance in AML and discuss emerging therapeutic strategies aimed at selectively targeting these cells. A deeper understanding of LSC biology will be critical for the development of combination therapies capable of eradicating minimal residual disease and achieving durable remission in patients with AML.