The classical definition of adult tissue stem cells (TSC) is fundamentally based on a functional perspective. A TSC is an undifferentiated cell, capable of proliferation, self-renewal, production of a large number of differentiated functional progeny, regenerating tissue after injury and a flexibility in the use of these options. Here, we discuss the necessity for amending this definition in the light of recent insight into stem cell biology regarding stem cell heterogeneity, lineage plasticity, clonal fluctuation and cell-environment interactions. We conclude that the definition needs amendments. A decade ago the flexibility criterion has attracted little attention but recent findings have indicated its importance. Flexibility and reversibility of tissue and lineage specification (tissue plasticity) and of properties within a tissue (within-tissue plasticity) have major implications with regard to concepts of stem cell function. We advocate to give up the view of TSC as being entities with a preprogrammed development and to replace it by a concept that makes the capabilities for flexible and regulated tissue self-organization based on cell-cell and cell-environment interactions the new paradigm. This concept would permit to incorporate the context-dependent lineage plasticity, within-lineage plasticity and generation of stem cell heterogeneity as a result of a dynamically regulated process. Such concepts need a rigorous examination by formal modeling including simulation studies. We provide some general ideas on how to proceed with such theories and illustrate this with worked models for tissue stem cells of the hematopoietic system and the intestinal epithelium.