This advanced research monograph is devoted to the Wiener-Hopf technique, a function-theoretic method that has found applications in a variety of fields, most notably in analytical studies of diffraction and scattering of waves. It provides a comprehensive treatment of the subject and covers the latest developments, illustrates the wide range of possible applications for this method, and includes an extensive outline of the most powerful analytical tool for the solution of diffraction problems. This will be an invaluable compendium for scientists, engineers and applied mathematicians, and will serve as a benchmark reference in the field of theoretical electromagnetism for the foreseeable future.