Because of the importance of the hydrogen bond, there have been scores of insights gained about its fundamental nature by quantum chemical computations over the years. Such methods can probe subtle characteristics of the electronic structure and examine regions of the potential energy surface that are simply not accessible by experimental means. The maturation of the techniques, codes, and computer hardware have permitted calculations of unprecedented reliability and rivaling the accuracy of experimental data. This book strives first toward an appreciation of the power of quantum chemistry to analyze the deepest roots of the hydrogen bond phenomenon. It offers a systematic and understandable account of decades of such calculations, focusing on the most important findings. This book provides readers with the tools to understand the original literature, and to perhaps carry out some calculations of their very own on systems of interest.