The fields of chemistry and graph theory have been inextricably linked for two centuries. The chemical structure that is the lingua franca is simply a graph theoretic notation. Here, a history of graph theory from the foundations of the wider field to the links with chemistry will be introduced. The early pioneers of graph theory and atomistic theory in chemistry will be discussed, with regard to how the chemical structure as we understand it today emerged and developed, and how mathematical graph theory was used to answer questions in chemistry. Mathematical chemistry will be introduced as a discipline and a review of some of the key pioneering work in this field will be provided. Graph theory is integral to many of the representations, descriptors, algorithms, and methodologies that appear later in this book, and this is an important background to the pioneers of these representations.