This paper provides a systematic and comprehensive study of the underlying semantics of temporal databases, summarizing the results of an intensive collaboration between the two authors over the last five years. We first examine how facts may be associated with time, most prominently with one or more dimensions of valid time and transaction time. One common case is that of a bitemporal relation, in which facts are associated with timestamps from exactly one valid-time and one transaction-time dimension. These two times may be related in various ways, yielding temporal specialization. Multiple transaction times arise when a fact is stored in one database, then later replicated or transferred to another database. By retaining the transaction times, termed temporal generalization, the original relation can be effectively queried by referencing only the final relation. We attempt to capture the essence of time-varying information via a very simple data model, the bitemporal conceptual data model. Emphasis is placed on the notion of snapshot equivalence of the information content of relations of different data models. The logical design of temporal databases is a natural next topic. Normal forms play a central role during the design of conventional relational databases. We show how to extend the existing relational dependency theory, including the dependencies themselves, keys, normal forms, and schema decomposition algorithms, to apply to temporal relations. However, this theory does not fully take into account the temporal semantics of the attributes of temporal relations. To address this deficiency, we study the semantics of individual attributes. One aspect is the observation and update patterns of attributes—when an attribute changes value and when the changes are recorded in the database, respectively. A related aspect is when an attribute has some value, termed its lifespan. Yet another aspect is the values themselves of attributes—how to derive a value for an attribute at any point in time from stored values, termed temporal derivation. This study of attribute semantics leads to the formulation of temporal guidelines for logical database design.