There is increasing evidence for the "cancer stem cell (CSC) hypothesis", which holds that cancers are driven by a cellular component that has stem cell properties, including self-renewal, tumorigenicity and multi-lineage differentiation capacity. Researchers and oncologists see in this model an explanation as to why cancer may be so difficult to cure, as well as a promising ground for novel therapeutic strategies. Given the specific stem cell features of self-renewal and differentiation, which drive tumorigenesis and contribute to cellular heterogeneity, each marker and assay designed to isolate and characterize CSCs has to be functionally validated. In this review, we survey tools and markers available or promising to identify breast CSCs. We review the main models used to study breast CSCs and how they challenge the CSC hypothesis.