This video is the best description I have yet seen on a very important NextGen-related trial the FAA is conducting, along with a wide array of other partners on both sides of the Atlantic. The trial is part of the Atlantic Interoperability Initiative to Reduce Emissions (known as AIRE), which is a joint effort between FAA and SESAR.
The full video can be seen here. But basically, it describes two things: the use of optimum flight paths on transatlantic routes, and tailored arrivals at Miami International Airport. Airlines such as American, Air France and Lufthansa are seeing great fuel saving results from both parts of the trial. Check it out -- we'll be seeing a lot more of this type of thing around the airspace system.