You can be eligible for foreign earned income exclusions (FEIE) and/or foreign income tax credits if you're a U.S. citizen residing abroad. Both contribute to lowering or eliminating US tax obligations. Publication 54, Tax Guide for U.S. Citizens and Resident Aliens Abroad, is a good resource for further information. The aforementioned article covers particular tax regulations for Americans who work overseas and receive income from other nations.
You can also be eligible for the foreign housing deduction and the foreign earned income exclusion if you fulfill the conditions. If qualified, you can avoid paying any taxes on up to around $105,000 (annually adjusted for inflation) of your income.