I moved to Canada 12 years ago from the US and am now a dual citizen. The US taxes its citizens based on citizenship, not residency, and you
must file US tax forms every year, no matter where you live. There are specific forms for Foreign Income and Foreign Tax Credit to fill out in addition to the normal 1040 and assorted schedules you'd use while living in the US. Depending on the country and whether or not there's a tax treaty between it and the US, you may end up owing no tax to the US, but you still have to file.
See
Publication 54, Tax Guide for U.S. Citizens and Resident Aliens Abroad for more details.