There is high clinical need for an adequate reconstruction of soft tissue defects as found after tumor resections, deep burns or severe trauma. A promising solution for these defects is adipose tissue engineering, with adult stem cells of the adipose tissue, implanted on 3D biomaterials. These adipogenic precursor cells survive ischemia better than mature adipocytes and have the potency to proliferate and differentiate into fat cells after transplantation. They can be yielded from excised adipose tissue or liposuction material. When preadipocytes are seeded on carriers for the generation of adipose tissue, chemical composition, mechanical stability and 3D architecture of the construct are crucial factors. They ensure cellular penetration into the construct, sufficient proliferation on the material and full differentiation inside the construct after transplantation. In hydrogels, it is especially the use and combination of growth factors that determine the overall outcome of the applied biopolymer. Over recent years, in vivo trials in particular have allowed significant insights into the potential, the perspectives, but also the current difficulties and draw-backs in adipose tissue engineering. This review focuses on the main strategies in adipose tissue regeneration, compares the various materials that have been used as carrier matrices so far and considers them in light of the challenges they have yet to meet.