The need for non-destructive testing/structural health monitoring (SHM) is becoming increasingly important for gas turbine manufacturers. Incipient cracks have to be detected before catastrophic events occur. With respect to condition-based maintenance, the complex and expensive parts should be used as long as their performance or integrity is not compromised. In this study, the main failure modes of turbines are reported. In particular, we focus on the turbine blades, turbine vanes and the transition ducts of the combustion chambers. The existing monitoring techniques for these components, with their own particular advantages and disadvantages, are summarised in this review. In addition to the vibrational approach, tip timing technology is the most used technique for blade monitoring. Several sensor types are appropriate for the extreme conditions in a gas turbine, but besides tip timing, other technologies are also very promising for future NDT/SHM applications. For static parts, like turbine vanes and the transition ducts of the combustion chambers, different monitoring possibilities are identified and discussed.