The active sites of heterogeneous catalysts can be difficult to identify and understand, and, hence, the introduction of active sites into catalysts to tailor their function is challenging. During the past two decades, scaling relationships have been established for important, heterogeneous catalytic reactions. More specifically, a physical or chemical property of the reaction system, termed as a reactivity descriptor, scales with another property often in a linear manner, which can describe and/or predict the catalytic performance. In this Review, we describe scaling relationships and reactivity descriptors for heterogeneous catalysis, including electronic descriptors represented by d-band theory, structural descriptors, which can be directly applied to catalyst design, and, ultimately, universal descriptors. The prediction of trends in catalytic performance using reactivity descriptors can enable the rational design of catalysts and the efficient screening of high-throughput catalysts. Finally, we outline methods to break scaling relationships and, hence, to break the constraint that active sites pose on the catalytic performance.