Sarcomas represent an extensive group of divergent malignant diseases, with the only common characteristic of being derived from mesenchymal cells. As such, sarcomas are by definition very heterogeneous, and this heterogeneity does not manifest only upon intertumoral comparison on a bulk tumor level but can be extended to intratumoral level. Whereas part of this intratumoral heterogeneity could be understood in terms of clonal genetic evolution, an essential part includes a hierarchical relationship between sarcoma cells, governed by both genetic and epigenetic influences, signals that sarcoma cells are exposed to, and intrinsic developmental programs derived from sarcoma cells of origin. The notion of this functional hierarchy operating within each tumor implies the existence of sarcoma stem cells, which may originate from mesenchymal stem cells, and indeed, mesenchymal stem cells have been used to establish several crucial experimental sarcoma models and to trace down their respective stem cell populations. Mesenchymal stem cells themselves are heterogeneous, and, moreover, there are alternative possibilities for sarcoma cells of origin, like neural crest-derived stem cells, or mesenchymal committed precursor cells, or - in rhabdomyosarcoma - muscle satellite cells. These various origins result in substantial heterogeneity in possible sarcoma initiation. Genetic and epigenetic changes associated with sarcomagenesis profoundly impact the biology of sarcoma stem cells. For pediatric sarcomas featuring discrete reciprocal translocations and largely stable karyotypes, the translocation-activated oncogenes could be crucial factors that confer stemness, principally by modifying transcriptome and interfering with normal epigenetic regulation; the most extensively studied examples of this process are myxoid/round cell liposarcoma, Ewing sarcoma, and synovial sarcoma. For adult sarcomas, which have typically complex and unstable karyotypes, stemness might be defined more operationally, as a reflection of actual assembly of genetically and epigenetically conditioned stemness factors, with dedifferentiated liposarcoma providing a most thoroughly studied example. Alternatively, stemness can be imposed by tumor microenvironment, as extensively documented in osteosarcoma. In spite of this heterogeneity in both sarcoma initiation and underlying stemness biology, some of the molecular mechanisms of stemness might be remarkably similar in diverse sarcoma types, like abrogation of classical tumor suppressors pRb and p53, activation of Sox-2, or inhibition of canonical Wnt/β-catenin signaling. Moreover, even some stem cell markers initially characterized for their stem cell enrichment capacity in various carcinomas or leukemias seem to function quite similarly in various sarcomas. Understanding the biology of sarcoma stem cells could significantly improve sarcoma patient clinical care, leading to both better patient stratification and, hopefully, development of more effective therapeutic options.