Cancer is characterized by a remarkable intertumoral, intratumoral, and cellular heterogeneity that might be explained by the cancer stem cell (CSC) and/or the clonal evolution models. CSCs have the ability to generate all different cells of a tumor and to reinitiate the disease after remission. In the clonal evolution model, a consecutive accumulation of mutations starting in a single cell results in competitive growth of subclones with divergent fitness in either a linear or a branching succession. Acute lymphoblastic leukemia (ALL) is a highly malignant cancer of the lymphoid system in the bone marrow with a dismal prognosis after relapse. However, stabile phenotypes and functional data of CSCs in ALL, the so-called leukemia-initiating cells (LICs), are highly controversial and the question remains whether there is evidence for their existence. This review discusses the concepts of CSCs and clonal evolution in respect to LICs mainly in B-ALL and sheds light onto the technical controversies in LIC isolation and evaluation. These aspects are important for the development of strategies to eradicate cells with LIC capacity. Common properties of LICs within different subclones need to be defined for future ALL diagnostics, treatment, and disease monitoring to improve the patients' outcome in ALL.