The purpose of this book is twofold: first, to introduce the reader to a wealth of concepts currently used for the description of quantum electrodynamic bound states, and second, to provide an overview of the current status of theory with respect to a number of physical effects that can be probed to utmost accuracy in high-precision experiments. The book is thus designed to provide both an opportunity for theoreticians to become acquainted with the intricacies of the bound-state formalism, and with the novel ideas that have been introduced over the last two decades in particular, while allowing experimentalists to learn about the current status of theory with respect to a number of phenomena.