This reprint is devoted to the 75th anniversary of the Casimir effect, and it covers the current status of both theoretical and experimental investigations in this quickly developing field of physics. The Casimir effect is unique in its multidisciplinary character. Its applications range from elementary particle physics, gravitation, and cosmology to atomic physics, condensed matter physics, and nanotechnology. This reprint is of interest for both the experts in these fields and the graduate and Ph.D. students who are going to conduct their research on different aspects of Casimir physics.