Adipose tissue is a rich, ubiquitous and easily accessible source for multipotent stromal/stem cells and has, therefore, several advantages compared to other sources of mesenchymal stromal/stem cells. Several studies have tried to identify the origin of the stromal/stem cell population within adipose tissue in situ. This is a complicated attempt because no marker has currently been described which unambiguously identifies native adipose-derived stromal/stem cells (ASCs). Isolated and cultured ASCs are a non-uniform preparation consisting of several subsets of stem and precursor cells. Cultured ASCs are characterized by their expression of a panel of markers (and the absence of others), whereas their in vitro phenotype is dynamic. Some markers were expressed de novo during culture, the expression of some markers is lost. For a long time, CD34 expression was solely used to characterize haematopoietic stem and progenitor cells, but now it has become evident that it is also a potential marker to identify an ASC subpopulation in situ and after a short culture time. Nevertheless, long-term cultured ASCs do not express CD34, perhaps due to the artificial environment. This review gives an update of the recently published data on the origin and phenotype of ASCs both in vivo and in vitro. In addition, the composition of ASCs (or their subpopulations) seems to vary between different laboratories and preparations. This heterogeneity of ASC preparations may result from different reasons. One of the main problems in comparing results from different laboratories is the lack of a standardized isolation and culture protocol for ASCs. Since many aspects of ASCs, such as the differential potential or the current use in clinical trials, are fully described in other recent reviews, this review further updates the more basic research issues concerning ASCs' subpopulations, heterogeneity and culture standardization.