Soft-tissue loss resulting from trauma or oncologic resection is a significant problem worldwide. Surgical reconstruction using adipose tissue has long been the gold-standard solution. However, these surgeries are often highly morbid, not always feasible in patients with insufficient adipose, and can have unpredictable results. Engineered soft-tissue replacements present a promising alternative. Many cell types, such as adipose-derived stem cells, have been recognized as a viable starting platform upon which new avenues in tissue engineering can be built. Additionally, efforts to develop scaffolds that can mimic the native extracellular matrix have been made with varying success. However, the suboptimal vascularization of engineered replacements is still a major limiting factor for achieving clinical translation. The current research explores the integration of all these techniques, including the use of growth factors, bioactive molecules, and advanced microsurgical techniques to enhance the vascularization process. This translational review covers the clinically standard methods of soft-tissue reconstruction and dives into emerging engineering techniques to develop vascularized adipose alternatives.