Standards-based, computable knowledge representations for eligibility criteria are increasingly needed to provide computer-based decision support for automated research participant screening, clinical evidence application, and clinical research knowledge management. We surveyed the literature and identified five aspects of eligibility criteria knowledge representation that contribute to the various research and clinical applications: the intended use of computable eligibility criteria, the classification of eligibility criteria, the expression language for representing eligibility rules, the encoding of eligibility concepts, and the modeling of patient data. We consider three of these aspects (expression language, codification of eligibility concepts, and patient data modeling) to be essential constructs of a formal knowledge representation for eligibility criteria. The requirements for each of the three knowledge constructs vary for different use cases, which therefore should inform the development and choice of the constructs toward cost-effective knowledge representation efforts. We discuss the implications of our findings for standardization efforts toward knowledge representation for sharable and computable eligibility criteria.