The contributors of this volume are working at the forefront of various realizations of quantum computers. They survey the recent developments in each realization, in the context of the Di Vincenzo criteria, including nuclear magnetic resonance, Josephson junctions, quantum dots, and trapped ions. There are also some theoretical contributions which have relevance in the physical realizations of a quantum computer. This book fills the gap between elementary introductions to the subject and highly specialized research papers to allow beginning graduate students to understand the cutting-edge of research in the shortest possible time.