Americans have discovered that one of the most powerful peacekeeping tools is money. Cash. It's not buying peace, as much as it is making friends and gaining access. In Iraq and Afghanistan, military commanders were given large sums of cash, to be spent as they saw fit for aid and reconstruction projects. This was most energetically practiced in Iraq, where large quantities of Saddam's cash (hundreds of millions in hundred dollar bills) was discovered by troops. Rather than ship it back to the U.S., commanders were allowed to use it. As a weapon. Anyway they could.
You can't do this sort of thing unless you have capable and trustworthy officers. This was the case, and American commanders got excellent results. The same policy was applied to Afghanistan. In both cases, the countries were poor and what political power there was resided in local tribal and religious leaders. When American troops enter the scene, the locals immediately understand that the combat unit commanders (usually a lieutenant colonel commanding a battalion or a colonel commanding a brigade) have a similar function to the sheikhs (in Iraq) or amirs (in Afghanistan). Like the tribal leaders, the Americans have a lot of guys with guns who respect and obey their leader.
In Iraq and Afghanistan, the tribal leader maintains his position with the power of his rank and stature, and money. You got a problem, you go to your tribal chief and ask for help. Much like the fictional mafia boss, Don Corleone. He does you a favor, then you owe him one. Most American commanders picked up on this tribal politics right away, and some of them proved very able at the haggling and negotiating that ensued when they met with tribal leaders and other locals seeking help.
Those commanders with lots of cash, and a head for putting it to good use, accomplished a lot. Some brigades quickly pacified their areas, while neighboring brigades still had a lot of angry people with guns to contend with. The U.S. Army is now using this experience to teach commanders how to get the best results. Not every army officer has the Don Corleone gene, but all can learn some basic procedures. If any commander uses his intel people to find out who the local worthies are, arranges meetings, gives out some goodies (usually in the form of building projects that generate jobs) and asks for something in return (information, or security from attack), the money is well spent. In the end, lives are saved, relationships built and fond memories created.
There are a lot of pitfalls. Some of the local leaders are scoundrels. They are out to fleece the rich foreigners, and will lie and cheat to accomplish this. Some commanders are really unsure of themselves when it comes to all this palavering with foreigners. Combat commanders are trained to lead men in battle, not discuss road building and pediatric medical care with conniving tribal chieftains. Making this work also requires follow-up and diplomacy. Corruption is common, and you lose points with the locals if your gifts are stolen by tribal chiefs (who then blame it on the foreigners). Many American commanders find this aspect of the job unsavory, and it is. But if you show the locals that you are now only a powerful military commander, but also a wily one, you gain respect and cooperation.
Commanders are also being taught local customs, and given tips by successful commanders who have preceded them. All of this is not really new. Over the past few centuries, American military commanders have employed the same techniques both at home and abroad. But the knowledge has generally been left out of officer training. This time, it may stay.