Physics-based representations constructed using only atomic positions and nuclear charges (also known as quantum machine learning, QML) allow for the reliable and efficient inference of molecular properties from training data. Chemistry is a science rooted in chemical reactions, naturally involving multiple molecular species. Here, we extend QML's capabilities to include the prediction of reaction properties by defining reaction representations: representations taking as input multiple molecules participating in a reaction, each represented by their corresponding atomic charges and three-dimensional coordinates. Several reaction representations are constructed from established molecular ones and benchmarked on four datasets representative of thermodynamic or kinetic reaction properties. One of these, the Hydroform-22-TS dataset (2350 energy barriers), is introduced as part of this work. The relevant ingredients for a high-performing reaction representation are extracted and used to construct the Bond-Based Reaction Representation ((BR2)-R-2) for the prediction of quantum-chemical properties of chemical reactions. Finally, variations of (BR2)-R-2 with varying representation size vs. performance are provided.