Stem cells, identified several decades ago, started to attract interest at the end of the nineties when families of mesenchymal stem cells (MSCs), concentrated in the stroma of most organs, were found to participate in the therapy of many diseases. In cancer, however, stem cells of high importance are specific to another family, the cancer stem cells (CSCs). This comprehensive review is focused on the role and the mechanisms of CSCs and of their specific extracellular vesicles (EVs), which are composed of both exosomes and ectosomes. Compared to non-stem (normal) cancer cells, CSCs exist in small populations that are preferentially distributed to the niches, such as minor specific tissue sites corresponding to the stroma of non-cancer tissues. At niches and marginal sites of other cancer masses, the tissue exhibits peculiar properties that are typical of the tumor microenvironment (TME) of cancers. The extracellular matrix (ECM) includes components different from non-cancer tissues. CSCs and their EVs, in addition to effects analogous to those of MSCs/EVs, participate in processes of key importance, specific to cancer: generation of distinct cell subtypes, proliferation, differentiation, progression, formation of metastases, immune and therapy resistance, cancer relapse. Many of these, and other, effects require CSC cooperation with surrounding cells, especially MSCs. Filtered non-cancer cells, especially macrophages and fibroblasts, contribute to collaborative cancer transition/integration processes. Therapy developments are mentioned as ongoing preclinical initiatives. The preliminary state of clinical medicine is presented in terms of both industrial development and future treatments. The latter will be administered to specific patients together with known drugs, with the aim of eradicating their tumor growth and metastases.