How (often) are jet engines cleaned? In the on-board magazine of my today's flight, there was a report on how fuel efficient the airline flies. They accomplish this by new scitimar winglets,  daily optimized route planning, and regular cleaning of the jet engines.

I never heard about this cleaning. How and how often is it done?
It used to be done launching crushed walnut shells into the running engine and the blades are polished by the process.  Known as Coke Blasting.  The process is uncommon these days.  

Similarly they use a walnut shelll coated emery cloth to polish crankshafts after machining 

http://www.dennisdawson.com/jetblast.htm

It is still commonly done on industrial turbines apparently