The main focus of the book are the physical mechanisms behind the spontaneous formation of ordered nanostructures at semiconductor surfaces. These mechanisms are at the root of recent breakthroughs in advanced nanotechnology of quantum-wire and quantum-dot fabrication. Generic theoretical models are presented addressing formation of all basic types of nanostructures, including periodically faceted surfaces, arrays of step-bunches of equal heights and single- and multi-sheet arrays of both 2- and 3-D strained islands. Decisive experiments on both structural and optical characterization of nanostructures are discussed to verify theoretical models and link them to practical examples. The book also describes experimental tools in nanoengineering that enable one to intentionally control the parameters of self-organized nanostructures, such as chemical composition, shape, size, density and relative arrangement of quantum dots and wires. Practical applications of nanoepitaxial technologies are discussed in the framework of recent advances in quantum dot lasers.