Research being done on composites by both Airbus and Boeing. The 787 is basically the guinea pig as from now on due to weight and fuel savings composite aircraft will become the way to go.
The Airbus A-350 which is seen as the replacement of the A-330 series of aircraft will due in 2015? Will take composite aircraft a stage further I believe. Airbus already has a large order in the pipeline from Emirates and some other airlines.

The main issue as I see it is that because not enough is known about composite materials, and how stress plus high speed operations will affect the materials over the short and long term.
This is a learning process for all involved in both aircraft companies, lets just hope that they keep their eye firmly on the ball so to speak.