Multiple myeloma (MM) is a haematological malignancy characterized by the accumulation of clonal plasma cells (PCs) in the bone marrow (BM). Although novel therapeutic strategies have prolonged survival of patients, the disease remains difficult to treat with a high risk of relapse. The failure of therapy is thought to be associated with a persistent population of the so‐called MM stem cells or myeloma initiating cells (MIC) that exhibit tumour‐initiating potential, self‐renewal and resistance to chemotherapy. However, the population responsible for the origin and sustainability of tumour mass has not been clearly characterized so far. This review summarizes current myeloma stem cell concepts and suggests that high phenotypic and intra‐clonal heterogeneity, together with plasticity potential of MM might be other contributing factors explaining discrepancies among particular concepts and contributing to the treatment failure.