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Environmentally-extended input-output (EEIO) analysis provides a simple and robust method for evaluating the linkages between economic consumption activities and environmental impacts, including the harvest and degradation of natural resources. EEIO is now widely used to evaluate the upstream, consumption-based drivers of downstream environmental impacts and to evaluate the environmental impacts embodied in goods and services that are traded between nations. While the mathematics of input-output analysis are not complex, straightforward explanations of this approach for those without mathematical backgrounds remain difficult to find. This manuscript provides a conceptual and intuitive introduction to the goals of EEIO, the principles and mathematics behind EEIO analysis and the strengths and limitations of the EEIO approach. The wider adoption of EEIO approaches will help researchers and policy makers to better measure, and potentially decrease, the ultimate drivers of environmental degradation.