Registration-based encryption (RBE) is reviewed in this article. A taxonomy and comprehensive assessment criteria for RBE are first proposed. In the taxonomy, RBE schemes are assorted into registered identity-based encryption (RIBE) schemes, registered attribute-based encryption (RABE) schemes, and registered functional encryption (RFE). In accordance with cryptographically functional features, RBE is further divided into subcategories with regard to basic functionality, variability, accountability, efficient computation, and large scale.In addition, a systematical methodology for discussing and comparing existing ABE schemes is proposed. For each type of RBE, the corresponding scenario is presented and explained by concrete examples. Specifically, the syntax of RBE is given followed by the adversarial model and security goals. RBE schemes are discussed according to the design strategies and special features and are compared in the proposed assessment criteria with respect to security and performance. To our knowledge, this survey is the first one to make a comprehensive and holistic comparison. Finally, a number of open research challenges in ABE are pointed out.