Adipose tissue as a stem cell source is ubiquitously available and has several advantages compared to other sources. It is easily accessible in large quantities with minimal invasive harvesting procedure, and isolation of adipose-derived mesenchymal stromal/stem cells (ASCs) yields a high amount of stem cells, which is essential for stem-cell-based therapies and tissue engineering. Several studies have provided evidence that ASCs in situ reside in a perivascular niche, whereas the exact localization of ASCs in native adipose tissue is still under debate. ASCs are isolated by their capacity to adhere to plastic. Nevertheless, recent isolation and culture techniques lack standardization. Cultured cells are characterized by their expression of characteristic markers and their capacity to differentiate into cells from meso-, ecto-, and entodermal lineages. ASCs possess a high plasticity and differentiate into various cell types, including adipocytes, osteoblasts, chondrocytes, myocytes, hepatocytes, neural cells, and endothelial and epithelial cells. Nevertheless, recent studies suggest that ASCs are a heterogeneous mixture of cells containing subpopulations of stem and more committed progenitor cells. This paper summarizes and discusses the current knowledge of the tissue localization of ASCs in situ, their characterization and heterogeneity in vitro, and the lack of standardization in isolation and culture methods.