Speaker Kevin McCarthy on Tuesday directed top congressional Republicans to open an impeachment inquiry into President Biden, reversing his previous stance that such an investigation should be initiated only with a vote of the House.

In doing so, Mr. McCarthy leveled a series of accusations against Mr. Biden that he said amounted to a “picture of a culture of corruption” and warranted the House using its most potent investigative tool to try to make the case for removing the president.

A White House spokesman noted that Republicans had “turned up no evidence of wrongdoing” and accused Mr. McCarthy of embracing “extreme politics at its worst.”

Here is what we know about the seven accusations Mr. McCarthy made against Mr. Biden on Tuesday, and how they line up with the facts of what Republicans have — and have not — uncovered so far.

Mr. McCarthy’s claim: “President Biden did lie to the American people about his own knowledge of his family’s foreign business dealings.”

The facts: It is not clear whether Mr. Biden willfully misrepresented his son Hunter Biden’s business dealings. The most prominent incorrect statement he has made on the matter came during a presidential debate in 2020, when he claimed that his son had not made money in China. It has since been revealed that he had.

In 2019, Mr. Biden repeatedly said he had “never discussed” and had “never spoken to” Hunter about his business dealings, and Republicans have produced no evidence that he was ever briefed on specific transactions or deals.

House Republicans have uncovered proof that the elder Mr. Biden was aware of and met some of his son’s business partners, raising questions about whether the president’s statements were misleading. But a key witness also testified that such conversations were superficial in nature, extending only to niceties like the weather or fishing.

In Hunter Biden’s book, he recounted how his father called him after Hunter joined the board of the Ukrainian energy company Burisma and warned, “I hope you know what you’re doing” — an acknowledgment of at least one conversation apparently unrelated to the details of any business dealings.

Mr. McCarthy’s claim: “Eyewitnesses have testified that the president joined on multiple phone calls, and had multiple interactions, dinners” that “resulted in cars and millions of dollars into his sons and his son’s business partners.”

The facts: Republicans have found evidence that Hunter Biden and his business partners engaged in a high-flying lifestyle, thanks to the wealth they had flowing in from their overseas business. For instance, an associate of Hunter Biden’s confirmed that he had received a wire of $142,300 from Kenes Rakishev, a Kazakh businessman, to pay for an expensive car.

Beyond Mr. Biden exchanging niceties with associates of his son, Republicans have provided no evidence that the elder Mr. Biden was involved in landing that business or participated in it in any way.

Mr. McCarthy’s claim: “We know that bank records show that nearly $20 million in payments were directed to the Biden’s family members and associates through various shell companies.”

The facts: Republicans have records that reflect that the Bidens, including Hunter Biden and the president’s brother Jimmy Biden, received millions of dollars from overseas business interests, but that total includes money that went to associates, not exclusively to family members. They have produced no evidence that any of the business relationships — such as Hunter’s seat on the Burisma board — were illegal.

Republicans have also pointed to the fact that Hunter Biden and his associates formed limited liability corporations to accuse them of creating “shell companies.” But such entities are common in new business ventures.

Mr. McCarthy’s claim: “The Treasury Department alone has more than 150 transactions involving the Biden family and other business associates that were flagged as suspicious activity by U.S. banks.”

The facts: House Republicans have reviewed so-called suspicious activity report records pertaining to Biden family business transactions. Those reports are described as “preliminary and unverified tip-and-lead information” that banks are required to file for any transaction that could potentially be a red flag for money laundering, including any cash transaction of more than $10,000.

Senate investigators and the Justice Department also reviewed such reports, but they did not result in any criminal charges.

Mr. McCarthy’s claim: “Even a trusted F.B.I. informant has alleged a bribe to the Biden family.”

The facts: The F.B.I. received an unverified allegation that Mr. Biden, while vice president, and Hunter Biden each accepted a $5 million bribe from a Burisma official. It has since been undercut by other evidence, including by the Ukrainian businessman who is alleged to have been involved and said that no such bribe occurred.

Mr. McCarthy’s claim: “Biden used his official office to coordinate with Hunter Biden’s business partners about Hunter’s role in Burisma.”

The facts: This refers to 2015 emails between a former Biden spokeswoman and a business associate of Hunter Biden discussing how to respond to an article in The New York Times. In a statement, the spokeswoman said that Mr. Biden had no involvement with his son’s company and that he had pushed for years for Ukraine to investigate and prosecute corruption.

Mr. McCarthy’s claim: “Finally, despite the serious allegations, it appears that the president’s family has been offered special treatment by Biden’s own administration, treatment that not otherwise would have” been “received if they were not related to the president.”

The facts: I.R.S. investigators who were scrutinizing Hunter Biden’s taxes testified that their inquiry was slow-walked and stonewalled at times. But they also said many of their complaints arose during the Trump administration, and they made no allegation that President Biden had tried to impede the inquiry.