Excess adiposity is the main phenotypic feature that defines human obesity and that plays a pathophysiological role in most chronic diseases. Measuring the amount of fat mass present is thus a central aspect of studying obesity at the individual and population levels. Nevertheless, a consensus is lacking among investigators on a single accepted ‘reference’ approach for quantifying fat mass in vivo. While the research community generally relies on the multi-component body volume class of ‘reference’ models for quantifying fat mass, no definable guide discerns among different applied equations for partitioning the four (fat, water, protein and mineral mass) or more quantified components, standardizes ‘adjustment’ or measurement system approaches for model-required labelled water dilution volumes and bone mineral mass estimates, or firmly establishes the body temperature at which model physical properties are assumed. The resulting differing reference strategies for quantifying body composition in vivo leads to small, but under some circumstances, important differences in the amount of measured body fat. Recent technological advances highlight opportunities to expand model applications to new subject groups and measured components such as total body protein. The current report reviews the historical evolution of multi-component body volume-based methods in the context of prevailing uncertainties and future potential.