Our goal has been to produce a useful resource for experts in the field as well as beginners, and also for those who simply want to acquaint themselves with this portion of Banach space theory. We have tried to provide some history of the subject, some of the important results, some flavor of the wide variety of methods used in attacking the characterization problem for varioustypes of spaces, and an exhaustive bibliography. We have probably underestimated the enormity of such a project, and perhaps what we have produced is more of a sampler than a full-blown survey.