Tap testing (initially) has been the cheapest method for testing composite structures. Damage is inferred from audible differences in the structure.This is an art as much as a science and is prone to human error. In safety critical areas this might result in greater expense based upon a conservative approach to judging the health of a part or a structure (replace rather than assume OK - false positives).
Thermographic and ultrasonic testing is also used in many cases (particularly if visual/tap inspection shows problems like debonding).
Currently a new range of non destructive inspection techniques (NDI) is evolving e.g. a test program is running under the auspices of the FAA and this is resulting in the definition of standards for testing composite laminates etc. The aim of defining standards is to allow the continued use of standard tools without impacting day to day operations while ensuring safety, reducing false positives and keeping costs within industry tolerances.
Tools like the Boeing MAUS system (resonance mode) are used to test composite materials in a number of industries.
The following PDF gives an insight into what people like NASA and the FAA are doing to ensure safety right across the fleet spectrum including next generation aircraft using a high % (by weight) of composite materials.
http://www.aeronautics.nasa.gov/nra_...al_plan_c1.pdf