How does the U.S. tax the salary I earned abroad before I moved here this year?

It depends on your U.S. tax residency status for that year. If you were a nonresident alien until your residency start date and became a resident alien partway through, you are typically a dual-status filer. In that case the U.S. generally taxes only the income you earned after your residency started, plus certain U.S.-source income during the nonresident portion; the salary earned abroad before you arrived is usually not U.S.-taxable. If, however, you elect to be treated as a full-year resident, for example to file jointly with a spouse, your entire year's worldwide income becomes U.S.-taxable, though the Foreign Tax Credit can offset foreign tax already paid. Which path is cheaper varies. The dual-status and first-year-choice rules are intricate, so review IRS Publication 519 or consult a cross-border preparer.