This article is the first of a two‐part series that describes and compares the essential features of nine existing “physical economy” approaches for quantifying the material demands of the human economy upon the natural environment. A range of material flow analysis (MFA) and related techniques is assessed and compared in terms of several major dimensions. These include the system boundary identification for material flow sources, extents, and the key socioinstitutional entities containing relevant driving forces, as well as the nature and detailing of system components and flow interconnections, and the comprehensiveness and types of flows and materials covered.Shared conceptual themes of a new wave of physical economy approaches are described with a brief overview of the potential applications of this broad family of methodologies. The evolving and somewhat controversial nature of the characteristics and role that define MFA is examined. This review suggests the need to specify whether MFA is a general metabolic flow measurement procedure that can be applied from micro to macrolevels of economic activity, or a more specific methodology aimed primarily at economy‐wide analyses that “map” the material relations between society and nature. Some alternative options for classifying MFA are introduced for discussion before a more detailed comparative summary of the key methodological features of each approach in the second part of this two‐part article.The review is presented (1) as a reference and resource for the increasing number of policy makers and practitioners involved in industrial ecology and the evaluation of the material basis of economies and the formulation of eco‐efficiency strategies, and (2) to provoke discussion and ongoing dialogue to clarify the many existing areas of discordance in environmental accounting related to material flows, and help consolidate the methodological basis and application of MFA.