Defects and impurities are critically influencing the properties of materials. Increase in computing power and the development of efficient algorithms indicate a promising future for computational defect science. This book surveys recent advances in electronic structure methods. The application of hybrid functionals, the LDA+U method, time-dependent DFT, quantum Monte Carlo, and many-body perturbation theory are described and assessed. Methods to treat large systems and temperature effects, as well as finite size effects in modeling are also reviewed. The book provides an introduction for novices and a guidance for practitioners in theoretical and computational defect physics.The editor, all authorities in this field, have selected respected scientists as chapter authors to provide and expert view of the latest advances. The result is a clear overview of the connections and boundaries between methods, as well as the broad criteria determining the choice between them for a given problem.