Like what somebody else said, they can improve either the sucking, squeezing, banging, or blowing :P
Improvement in sucking can be done by improving the fan at the front. Nowadays, in the new engine designs, we've got massive diameter, variable/chord, composite, forward fans.
(Turboprops are essentially jet engines with a propeller, which is a very large diameter fan in front.
There has also been talk about a pusher-type turboprop that would be even more efficient, without as much a loss in speed as turboprops)
Improvement in squeezing is being done with multiple stage, multiple gearboxes, multiple spool compressor stages, and lighter stronger materials
Improvement in banging is being accomplished by designing combustor cans that are more efficient and burn cleaner, like on the GE GEnx. Hopefully, perhaps in the future, they'll come up with some kind of additive to allow the fuel to burn cleaner, or come up with a new fuel that offers more energy density--bang for your buck--than jet A.
Improvement in blowing is being done in about the same way as sucking. Better fans, lighter and stronger materials, lower friction shafts and gearboxes leading back to the rest of the engine, etc.