Quantum mechanical methods are being used increasingly to probe the properties of materials. Of particular importance is the behavior of localized states - defects or impurities - which commonly control the spectroscopic transport, thermodynamic and mechanical properties of crystalline solids. Simulation methods based on effective potentials have had an important impact on this field. One of the objectives of the book is to illustrate that different methodologies can not only be used to investigate similar types of problems but that often complementary results are obtained.