Updates are essential in database applications that require reasoning under dynamic situations. The objective of the project is to enhance current database systems with strong capabilities ofmodeling and processing changes. An update calculus and an update algebra have been developed for specifying dynamic queries, and have been shown to be equivalent to each other. This project investigates algorithms for optimization and efficient evaluation of dynamic queries. Hypothetical queries are a special case in which new databases after updates are not needed for answers. Transformations of these queries into static ones are explored in order to take advantage of existing querying technology. This project also pursues simplification and inference techniques for consistency checking so that data integrity can be preserved after updates. Results of the project will extend database technology to a wider class of applications that exhibit complex dynamic behavior.