Besides bindings to the toolkit's (e.g. Qt's) API and the Squish script API, it is also possible to create script bindings for custom C++ API defined in the AUT or components of the AUT. This way it is possible to directly call such APIs from test scripts which allows accessing e.g. data structures of the application for verifications.
This powerful feature of Squish is described in detail in the tutorial Tutorial: Creating and Accessing Application Bindings (Chapter 11).