An outline of Gy's contributions to particulate material sampling is presented. Gy's theory provides a comprehensive framework that integrates all aspects of sampling particulate materials such as coal, ores, pulps, industrial and municipal effluents, and environmental contaminants. The theory defines and quantifies the two types of heterogeneity (constitution and distribution) and shows how they can be empirically measured using either expensive variographic information or often more readily available size—density information. These results provide principles for constructing sampling devices free from bias and excessive noise. They also provide practical methods for realistically estimating sampling precision for both increment processes (e.g. cross–stream samplers) and splitting processes (e.g. riffle splitters) without requiring significant additional work. The theory also provides practical methods for investigating the potential bias in sampling equipment and methods.