Patients suffering from acute myeloid leukemia (AML) show highly heterogeneous clinical outcomes. Next to variabilities in patient-specific parameters influencing treatment decisions and outcome, this is due to differences in AML biology. In fact, different genetic drivers may transform variable cells of origin and co-exist with additional genetic lesions (e.g., as observed in clonal hematopoiesis) in a variety of leukemic (sub)clones. Moreover, AML cells are hierarchically organized and contain subpopulations of more immature cells called leukemic stem cells (LSC), which on the cellular level constitute the driver of the disease and may evolve during therapy. This genetic and hierarchical complexity results in a pronounced phenotypic variability, which is observed among AML cells of different patients as well as among the leukemic blasts of individual patients, at diagnosis and during the course of the disease. Here, we review the current knowledge on the heterogeneous landscape of AML surface markers with particular focus on those identifying LSC, and discuss why identification and targeting of this important cellular subpopulation in AML remains challenging.