 Chemistry has traditionally distinguished itself from classical physics by its interest in the division of matter into different substances and in chemical combination, the process whereby substances are held together in compounds and solutions. In this section, we have described how chemists came to understand that all substances were composed of the Periodic Table’s elements, and that these elements are actual components of substances. Even with this knowledge, distinguishing pure substances from heterogeneous mixtures and solutions remained a very difficult chemical challenge. And despite chemists’ acceptance of the law of definite proportions as a criterion for substancehood, chemical complexities such as the discovery of the Berthollides muddied the waters.