Quantum computation is a field in which there is much current interest. Much of the recent material is published in conference proceedings which are not widely available. This review is written with the purpose of making the work in this field more widely available, and, hopefully, easier to understand. The language used will be closer to that used by physicists than is used in some of the reviewed papers. Background material on energy dissipation and reversibility of the computation process is summarized to given the framework in which the field developed. Aspects of quantum mechanics, which were much discussed in the literature as potential problems for construction of models of quantum computation, are also briefly reviewed. A good part of this review is concerned with work done in the 1980s, which forms the basis for the recent work. This includes quantum mechanical models of deterministic and nondeterministic Turing machines and quantum mechanical models of computation networks of deterministic and nondeterministic logic gates. Topics of recent work covered in this review include unsolvability aspects of the evolution operators for quantum computers, properties of universal quantum Turing machines, and quantum algorithms for solving problems more efficiently than classical computers. The emphasis here is in understanding how the algorithms use quantum coherence to carry out computations. The review concludes with a discussion of robustness and physical constructability of quantum computers.