United and Southwest recently started using Pratt and Whitney's EcoPower system for washing jet engines. Ecowash was first operational at Schipol (Amsterdam) about a year ago. Since it works on any kind of jet engine (not just P&W) and does save about 1% on fuel burn, I expect that within a year everyone will be using it. The system removes dirt and grime inside the engine, and improved engine operation is about 1%.
Previous systems involved either highly toxic chemicals or had substantial waste disposal problems. JFK and a few other airports had banned the approaches involving toxic chemicals. This system used just water jets, and has an internal wash recycling so that final waste disposal does not involve the general airport wastewater. The waste still needs disposal processing, but it's now just because of the engine grime itself, not solvents or detergents.