As others have said, you still have to fill in US tax returns.
I've just seen the book <em>U.S. Taxes for Worldly Americans: The Traveling Expat's Guide to Living, Working, and Staying Tax Compliant Abroad</em> mentioned on another sub - I have no idea how good it is, but it's free on Kindle right now. I assume this is a limited time offer.
Sometimes people just don’t know the should file if they live abroad. The U.S. is one of only two countries in the world that taxes its people based on their citizenship, not on where they live or where their money comes from. If you make more than $10,350 per year (as of 2016) and are a U.S. Citizen, you still must file a return each year. Even if you can arrange things so that you legally owe nothing, you must still file.
If you’d like to know more, you can find the relevant book on Amazon: U.S. Taxes for Worldly Americans: The Traveling Expat's Guide to Living, Working, and Staying Tax Compliant Abroad https://www.amazon.com/U-S-Taxes-Worldly-Americans-Traveling-ebook/dp/B01N6PAE5Y/ref=sr_1_3?s=digital-text&ie=UTF8&qid=1487360085&sr=1-3&keywords=expat+tax. It explains how expats and most people who work overseas can legally lower their U.S. tax to $0 and keep their income and assets safe from the IRS.
I read the book, US Taxes for Worldly Americans, and the author has a tax service where they offer a free 20min consult. Worth it just to understand the options you have. They were super nice, and I plan on filing through them.