Adult neural stem cells (aNSCs) are the source for the continuous production of new neurons throughout life. This so-called adult neurogenesis has been extensively studied; the intermediate cellular stages are well documented. Recent discoveries have raised new controversies in the field, such as the notion that progenitor cells hold similar self-renewal potential as stem cells, or whether different types of aNSCs exist. Here, we discuss evidence for heterogeneity of aNSCs, including short-term and long-term self-renewing aNSCs, regional and temporal differences in aNSC function, and single cell transcriptomics. Reviewing various genetic mouse models used for targeting aNSCs and lineage tracing, we consider potential lineage relationships between Ascl1-, Gli1-, and Nestin-targeted aNSCs. We present a multidimensional model of adult neurogenesis that incorporates recent findings and conclude that stemness is a phenotype, a state of properties that can change with time, rather than a cell property, which is static and immutable. We argue that singular aNSCs do not exist.