What tax forms need to be filed for an irrevocable trust?

Form 1041 is U.S. Income Tax Return for Estates and Trusts. Trusts are required to file Form 1041 when (1) its income is at least $600, or (2) it has a nonresident alien as a beneficiary.

But a trust classified as a grantor trust isn't required to file Form 1041 if the individual grantor reports all the grantor trust incomes/allowable expenses on his own Form 1040. For tax purposes, an irrevocable trust is treated as a simple, complex, or grantor trust according to the powers listed in establishing the trust.