Michael Benedikt Bell Laboratories, 263 Shuman Blvd., Naperville, IL 60566 benedikt@research.bell-labs.com Title: Some Extensions of Finite Model Theory In this talk I'll overview several extensions of finite model theory that combine an uninterpreted component with some fixed, interpreted structure. I'll concentrate on two extensions: the Metafinite model theory of Gurevich and Gradel, and the Embedded Finite Model Theory that comes out of the constraint database community.