The original 1913 Revenue Act only required the reporting of income from "lawful" sources. In the 1921 Revenue Act the word, "lawful" was removed requiring all income to be reported.
[IRS Publication 17] states:
Illegal activities. Income from illegal activities, such as money from dealing illegal drugs, must be included in your income on Form 1040, line 21, or on Schedule C or Schedule C-EZ (Form 1040) if from your self-employment activity.
In United States v. Sullivan in 1927, the U.S. Supreme Court ruled that it was constitutional to require that a tax return be filed to report income. If the filer believed information required to be filed would incriminate him then the filer could raise the issue on the form. The filer could not simply refuse to file.
Justice Holmes further wrote:
It is urged that, if a return were made, the defendant would be entitled to deduct illegal expenses, such as bribery. This by no means follows, but it will be time enough to consider the question when a taxpayer has the temerity to raise it.
In Garner v. United States in 1976, the Supreme Court ruled that a filer's income tax return that revealed himself to be a gambler could be used as evidence that the filer violated gambling laws.
An article in Forbes describes a taxpayer who filed their returns but refused to answer some questions related to their income, asserting a Fifth Amendment privilege.
The IRS attempted to impose a "frivolous return" penalty on the taxpayer for refusing to provide all information.
The Tax Court ruled that the taxpayer had a legitimate fear regarding disclosure of information related to failing to file a report of foreign bank and financial accounts.
The tax court found the taxpayer had filed the standard return, the return contained sufficient information and that a return doesn't need to be "completely correct" but, rather, "substantially correct."
The IRS had claimed that omitting some information because of fear of self-incrimination is frivolous.
The Tax Court found that the standard, Notice 2010-33, doesn't require that "all" information must be provided, simply that substantial information must be provided.
As a result, the penalty was removed and the taxpayer's assertion of Fifth Amendment privilege was found not to be "frivolous."
As the Tax Court ruling explains,
the Fifth Amendment privilege applies to tax returns, provided the taxpayer affirmatively claims the privilege on the return and does so before he files it.
In summary, it is still necessary to file a return; a blanket Fifth Amendment claim applying to the entire return is considered frivolous. However, the taxpayer must claim the privilege. Any incriminating information included on the return can be used against the taxpayer.