Recent advances in adipose tissue engineering and cell biology have led to the development of innovative therapeutic strategies in regenerative medicine for adipose tissue reconstruction. To date, the many in vitro and in vivo models developed for vascularized adipose tissue engineering cover a wide range of research areas, including studies with cells of various origins and types, polymeric scaffolds of natural and synthetic derivation, models presented using decellularized tissues, and scaffold-free approaches. In this review, studies on adipose tissue types with different functions, characteristics and body locations have been summarized with 3D in vitro fabrication approaches. The reason for the particular focus on vascularized adipose tissue models is that current liposuction and fat transplantation methods are unsuitable for adipose tissue reconstruction as the lack of blood vessels results in inadequate nutrient and oxygen delivery, leading to necrosis in situ. In the first part of this paper, current studies and applications of white and brown adipose tissues are presented according to the polymeric materials used, focusing on the studies which could show vasculature in vitro and after in vivo implantation, and then the research on adipose tissue fabrication and applications are explained.