White adipose tissue (WAT) is made by cells able to store lipids in order to provide fuel for the organism in the interval between meals. Brown adipose tissue (BAT) have a different function: burn lipids to produce heat. Our group developed recently a new concept regarding adipose tissues of mammals: the concept of the adipose organ. The innovative part of this concept try to give an explanation to the fact that WAT and BAT are contained mixed together into a dissectable organ formed by several subcutaneous and visceral depots. The reason why these two different tissues are mixed together is not clear and our concept of adipose organ offer an explanation: the two tissues are mixed together in the same organ because the two cell type are able to transdifferentiate reciprocally in order to answer to different requests of energy partitioning. The well known phenomenon of reversible, apparent, transformation of the adipose tissues following physiological stimuli such as cold exposure (the organ phenotype change from white to brown) , warm exposure (the organ phenotype change from brown to white), pregnancy-lactation (part of the organ phenotype change from white adipose tissue to milk-secreting glands) would be due to intrinsic biologic properties of adipocytes that are able to undertake a reversible transdifferentiation. This concept open new perspectives in the field of cell biology: the ability of differentiated cells of mammals to undergo a physiologic reversible transformation process that drive into a new phenotype (with new morphology and physiology). In this review we will describe the most important data obtained in our and other's laboratories supporting this new concept of the adipose organ with particular emphasis to data supporting the transdifferentiation as the main process at the base of its plasticity.