Adipose tissue is a specific variety of connective tissue; composed of a group of cells called adipocytes, specialised in storing fats. The adipose tissue consists of the joining, through reticular fibres, of the adipocytes forming lobes, between which run numerous blood vessels. Adipose tissue adult stem cells, termed stem cells or mesenchymal stem cells (MSCs), with the capacity for self-renewal and multipotential differentiation and can be harvested through surgery and direct excision, liposuction in the trunk and extremities as well as the Coleman technique for fat tissue transplantation and remodelling. The multipotentiality allows them to become adipocytes, chondrocytes, myocytes, osteoblasts and neurocytes among other cell lineages. Stem cells and, in particular, adipose tissue-derived cells, play a key role in reconstructive or tissue engineering medicine as they have already proven effective in developing new treatments.