The representation of chemical structures has a long and complicated history from the foundations of atomistic theory in the early nineteenth century through to the modern day of large and complex chemical information systems and databases. This chapter provides a history of the types of chemical structure systems used historically, and still to the current day, and the associated challenges in ensuring they are machine-readable. These challenges then take us to the modern day and the machine-readable chemical structure representations that are used widely in chemical information systems, including more substantive introductions to the most common representations used today. It is no overstatement to say that appropriate chemical structure representations are the foundation of all research in this field and are therefore an important subject area on which to spend time.