Obesity and associated diseases, such as diabetes, have reached epidemic proportions globally. In the era of 'diabesity' and due to its central role for metabolic and endocrine processes, adipose tissue (specifically white adipose tissue; WAT) has become a target of high interest for therapeutic strategies. To gain insights in cellular and molecular mechanisms of adipose (patho-)physiology, researchers traditionally relied on animal models since in vitro studies on human WAT are challenging due to the large size, buoyancy, and fragility of mature white adipocytes. Leveraging the Organ-on-Chip technology, we introduce a next-generation microphysiological in vitro model of human WAT based on a tailored microfluidic platform featuring vasculature-like perfusion. The platform integrates a 3D tissue comprising all major WAT-associated cellular components in an autologous manner, including not only mature adipocytes but also organotypic endothelial barriers and stromovascular cells featuring tissue-resident innate immune cells, specifically adipose tissue macrophages. This microphysiological tissue model recapitulates pivotal WAT functions, such as energy storage and mobilization as well as endocrine and immunomodulatory activities. The combination of all individual cell types with extra cellular matrix-like hydrogels in a precisely controllable bottom-up approach enables the generation of a multitude of replicates from the same donors circumventing issues of inter-donor variability and paving the way for personalized medicine. Moreover, it allows to adjust the model's degree of complexity to fit a specific purpose via a flexible mix-and-match approach with different cell component modules. This novel WAT-on-chip system constitutes a human- based, autologous and immunocompetent in vitro model of adipose tissue that recapitulates almost full tissue heterogeneity. In the future, the new WAT-on-chip model can become a powerful tool for human-relevant research in the field of metabolism and its associated diseases as well as for compound testing and personalized- and precision medicine applications.