Processing queries approximately is an effective way to reduce query response time in on-line support systems, especially when the precise answer is not necessary or early feedback is helpful. In an approximate query processing system, a query is answered based on the data synopses instead of the original data. The key of this research area is to develop effective synopses construction techniques. In this monograph, we will investigate various approximate query processing techniques developed in the relational database, spatio-temporal database and in the data stream environment.