We present an account of string field theory which aims to introduce the reader to the important concepts of the subject as well as to aid access to the literature. Light cone string theory is briefly reviewed, but the emphasis is on the covariant approach exploiting world sheet BRST invariance to define string field derivations, integration, and products. Although we try to present the ideas in a general way, we draw on Witten's formulation of open string field theory for most of our examples. We include brief self-contained reviews of both the operator and Lagrangian versions of the BRST formalism employed in this article. There is a detailed account of perturbation theory for Witten's theory, including a few explicit sample calculations. Open problems faced by open superstring field theory and by closed string field theory are discussed. We sketch some of the ideas for attacking them but do not give a definitive resolution. Finally, some new formulae relevant to the "bosonization of superghosts" are derived in a self-contained appendix.