Stem cells have been the focus of an intense research due to their potential in Regenerative Medicine, drug discovery, toxicology studies, as well as for fundamental studies on developmental biology and human disease mechanisms. To fully accomplish this potential, the successful application of separation processes for the isolation and purification of stem cells and stem cell-derived cells is a crucial issue. Although separation methods have been used over the past decades for the isolation and enrichment of hematopoietic stem/progenitor cells for transplantation in hemato-oncological settings, recent achievements in the stem cell field have created new challenges including the need for novel scalable separation processes with a higher resolution and more cost-effective. Important examples are the need for high-resolution methods for the separation of heterogeneous populations of multipotent adult stem cells to study their differential biological features and clinical utility, as well as for the depletion of tumorigenic cells after pluripotent stem cell differentiation. Focusing on these challenges, this review presents a critical assessment of separation processes that have been used in the stem cell field, as well as their current and potential applications. The techniques are grouped according to the fundamental principles that govern cell separation, which are defined by the main physical, biophysical, and affinity properties of cells. A special emphasis is given to novel and promising approaches such as affinity-based methods that take advantage of the use of new ligands (e.g., aptamers, lectins), as well as to novel biophysical-based methods requiring no cell labeling and integrated with microscale technologies.