Mammals have two types of adipocytes, white and brown, but their anatomy and physiology is different. White adipocytes store lipids, and brown adipocytes burn them to produce heat. Previous descriptions implied their localization in distinct sites, but we demonstrated that they are mixed in many depots, raising the concept of adipose organ. We explain the reason for their cohabitation with the hypothesis of reversible physiological transdifferentiation; they are able to convert one into each other. If needed, the brown component of the organ could increase at the expense of the white component and vice versa. This plasticity is important because the brown phenotype of the organ associates with resistance to obesity and related disorders. Another example of physiological transdifferetiation of adipocytes is offered by the mammary gland; the pregnancy hormonal stimuli seems to trigger a reversible transdifferentiation of adipocytes into milk-secreting epithelial glands. The obese adipose organ is infiltrated by macrophages inducing chronic inflamation that is widely considered as a causative factor for insulin resistance. We showed that the vast majority of macrophages infiltrating the obese organ are arranged around dead adipocytes, forming characteristic crown-like structures. We recently found that visceral fat is more infiltrated than the subcutaneous fat despite a smaller size of visceral adipocytes. This suggests a different susceptibility of visceral and subcutaneous adipocytes to death, raising the concept of smaller critical death size that could be important to explain the key role of visceral fat for the metabolic disorders associated with obesity.