User-defined aggregates are essential in many advanced database applications, particularly in expressing data mining functions, but they find little support in current systems including Object-Relational databases. Three serious limitations of current systems are (i) the inability of introducing new aggregates (e.g., by coding them in procedural language as originally proposed in SQL3), (ii) the inability of returning partial results during the computation (e.g., to support online aggregation), and (iii) the inability of using aggregates in recursive queries (e.g., to express Bill of Materials and optimized graph searches).In this paper, we presents a unified solution to these problems which realizes SQL3 original proposal for user-defined aggregates (U-DAs), and adds significant improvements in terms of expressive power and ease of use: in fact our SQL-AG system also supports online aggregation, monotonic aggregation, and a high-level aggregate definition language named SADL. We focus on applications of UDAs and SADL.