Whether they find evidence of crimes, however, will also depend on other information not found in the actual returns.

The United States Supreme Court on Monday cleared the way for the Manhattan district attorney, Cyrus R. Vance Jr., to obtain eight years of Mr. Trump’s federal income tax returns and other records from his accountants. The decision capped a long-running legal battle over prosecutors’ access to the information.

The New York Times last year provided more or less a preview of what awaits Mr. Vance, when it obtained and analyzed decades of income tax data for Mr. Trump and his companies. The tax records provide an unprecedented and highly detailed look at the byzantine world of Mr. Trump’s finances, which for years he has simultaneously bragged about and sought to keep secret.

The Times’s examination showed that the former president reported hundreds of millions of dollars in business losses, went years without paying federal income taxes and faces an Internal Revenue Service audit of a $72.9 million tax refund he claimed a decade ago.

Among other things, the records revealed that Mr. Trump had paid just $750 in federal income taxes in his first year as president and no income taxes at all in 10 of the previous 15 years. They also showed he had written off $26 million in “consulting fees” as a business expense between 2010 and 2018, some of which appear to have been paid to his older daughter, Ivanka Trump, while she was a salaried employee of the Trump Organization.

The legitimacy of the fees, which reduced Mr. Trump’s taxable income, has since become a subject of Mr. Vance’s investigation, as well as a separate civil inquiry by Letitia James, the New York attorney general. Ms. James and Mr. Vance are Democrats, and Mr. Trump has sought to portray the multiple inquiries as politically motivated, while denying any wrongdoing.

Mr. Vance’s office has issued subpoenas and conducted interviews in recent months as it scrutinizes a variety of financial matters, including whether the Trump Organization misrepresented the value of assets when obtaining loans or paying property taxes, as well as the payment of $130,000 in hush money during the 2016 campaign to Stephanie Clifford, the pornographic film actress whose stage name is Stormy Daniels. Among those interviewed have been employees of Deutsche Bank, one of Mr. Trump’s largest lenders.

For all their revelations, Mr. Trump’s tax records are also noteworthy for what they do not show, including any new details about the payment to Ms. Clifford, which was the initial focus of Mr. Vance’s investigation when it began two years ago.

The tax returns represent a self-reported accounting of revenues and expenses, and often lack the specificity required to know, for instance, if legal costs related to hush-money payments were claimed as a tax write-off, or if money from Russia ever moved through Mr. Trump’s bank accounts. The absence of that level of detail underscores the potential value of other records that Mr. Vance won access to with Monday’s Supreme Court decision.

In addition to the tax returns, Mr. Trump’s accountants, Mazars USA, must also produce business records on which those returns are based and communications with the Trump Organization. Such material could provide important context and background to decisions that Mr. Trump or his accountants made when preparing to file taxes.

John D. Fort, a former chief of the I.R.S. criminal investigation division, said tax returns were a useful tool for uncovering leads, but could only be fully understood with additional financial information obtained elsewhere.

“It’s a very key personal financial document, but it’s just one piece of the puzzle,” said Mr. Fort, a C.P.A. and the director of investigations with Kostelanetz & Fink in Washington. “What you find in the return will need to be followed up on with interviews and subpoenas.”

Still, The Times’s investigation of Mr. Trump’s returns exposed a number of misleading assertions and falsehoods he has propagated about his wealth and business acumen.