Soft tissue defects are a common clinical challenge mostly caused by trauma, congenital anomalies and oncological surgery. Current soft tissue reconstruction (STR) options include synthetic materials (fillers and implants) and autologous adipose tissue transplantation through flap surgery and/or lipotransfer. Both reconstructive options hold important disadvantages to which vascularized adipose tissue engineering (VATE) strategies could offer solutions. In this review, we first summarized pivotal characteristics of functional adipose tissue (FAT) such as the structure, function, cell types, development and extracellular matrix (ECM). Next, we discussed relevant cell sources and how they are applied in different state-of-the-art VATE techniques. Herein, biomaterial scaffolds and hydrogels, ECMs, spheroids, organoids, cell sheets, 3D bioprinting and microfluidics are overviewed. Also, we included extracellular vesicles and emphasized their potential role in VATE. Lastly, current challenges and future perspectives in VATE are pointed out to help to pave the road towards clinical applications.