Hydrogen is a common impurity in all semiconductors. Although it is sometimes deliberately introduced, hydrogen often penetrates into the crystal during device processing. It interacts with broken or weak covalent bonds, such as those found at extended and localized defect centers. The main results of these covalent interactions are shifts of energy levels out of (or into) the gap and new optical activity (infrared absorption and Raman scattering). The shifts in energy levels lead to the passivation (or activation) of the electrical activity of various centers. Hydrogen can also interact with the perfect crystal and with itself, sometimes leading to the formation of extended structures known as platelets. Finally, H also acts as a catalyst, dramatically enhancing the diffusivity of interstitial oxygen in Si. The consequences of these interactions are substantial changes in the electrical and optical properties of the crystal, and in the lifetime of charge carriers. The thermal stability of the complexes containing hydrogen varies from room temperature up to several hundreds of degrees Celsius, and the diffusion of H is trap-limited up to rather high temperatures. Hydrogen normally exists in more than one configuration and charge state in semiconductors. A range of experimental and theoretical techniques have been used to investigate the rich properties of hydrogen in semiconductors, and several extensive reviews focusing mostly on the experimental side of these issues have been published in the past five years. The present review focuses mostly on the theoretical work performed in this field. However, the most recent experimental results are also discussed, and the current understanding of hydrogen interactions in semiconductors summarized.