During the last few years, parallel object-relational database management systems have emerged as the leading data management technology on the market. These systems are extensible by user-defined data types and user-defined functionality for the data. This work focuses on the efficient parallel execution of user-defined functionality. The main contributions describe techniques to support data parallelism for user-defined scalar and aggregate functions and intra-function parallelism for the execution of a scalar function on a large object, and a new technology to provide extensibility with regard to new set-oriented database operations that can efficiently implement user-defined functionality in parallel object-relational database management systems.