The Democratic takeover of the House of Representatives gives the party new legal firepower to investigate the Trump administration, including the authority to demand the president’s tax returns and financial records. Once Democrats formally seize control of the House in January, the new chairmen and women of key congressional committees are expected to begin issuing subpoenas and launch investigations, and demanding that Trump administration officials testify publicly and under oath on multiple topics.

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Some of those demands are likely to face legal challenges from Trump’s team of lawyers, who will argue that certain information is protected by executive privilege.

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But Tuesday’s election results nevertheless puts the White House under intense new scrutiny, in addition to the ongoing criminal investigation that is already under way by the special counsel Robert Mueller into possible collusion between the Trump campaign and the Kremlin. What will Democrats pursue first?

Trump’s tax returns and banking records

The incoming chairwoman of the House financial services committee, Maxine Waters, is about to become a thorn in Trump’s side. She is expected to use her subpoena power to demand access to Trump’s tax returns from the US treasury and potentially his private banking records from Deutsche Bank, where executives are already preparing to be called to testify about their relationship with the president. Waters can also demand that the US treasury reveal information about suspicious financial transactions involving Trump and his team and the Kremlin. This line of questioning may lead to new information about Deutsche Bank’s dealings in Moscow and work on behalf of Russian oligarchs.

Trump’s personal enrichment and alleged corruption

Hours after it became clear that he was the next likely chairman of the House oversight committee, veteran congressman Elijah Cummings declared his intent to investigate Trump for allegedly enriching himself by having foreign leaders stay at the Trump Organization’s hotel in Washington. It is illegal under the US constitution’s emoluments clause for a president to accept payments from foreign leaders.

Russia investigation and obstruction of justice

For two years, questions in Congress about the Trump campaign’s possible collusion with the Kremlin to win the 2016 election has been controlled by Republicans. Now, Adam Schiff, the next chairman of the House intelligence committee, has vowed to make the issue his top priority, including a close examination of whether Russia has financial leverage over the president through its investments in Trump’s business empire. Schiff will probably have the support and cooperation of former intelligence and national security experts. He could also seek more information about whether Trump sought to obstruct the FBI’s investigation into the president’s dealings with Moscow when he fired the FBI director James Comey.

Brett Kavanaugh

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The confirmation of the new supreme court nominee was one of the most controversial episodes in the first two years of Trump’s presidency and one that is still surrounded by unanswered questions. Jerry Nadler, the incoming chairman of the House judiciary committee, has promised he would take another look at whether Brett Kavanaugh perjured himself during his confirmation hearings when he was asked about allegations of sexual assault. Other members of Congress have also raised questions about why two men initially came forward and suggested they had perpetrated an alleged assault against one of Kavanaugh’s accusers. Congressman Elijah Cummings, who will head the oversight committee, has suggested the apparently false confessions could have been part of a Republican effort to shield Kavanaugh. The FBI’s handling of its background check – called a “sham” by Democrats – will also likely face scrutiny.

Other investigations

Other possible lines of inquiry include: why former national security adviser Michael Flynn and Jared Kushner, the president’s son-in-law, were given security clearances upon entering the White House even though their access to classified information troubled some national security experts; how the Trump campaign spent millions of dollars in donations to its presidential inauguration; and whether the president’s former lawyer, Michael Cohen, improperly received corporate donations from AT&T and others in exchange for favours from the Trump administration.

The new thorns in Trump’s side

Maxine Waters

The incoming 79-year-old chairwoman of the House financial services committee has been a frequent target of Trump and derided as “low IQ”. We may soon understand why Trump dislikes her. Representing California, Waters has consistently demanded information about Trump’s private bank dealings and possible connections to Russia. She will soon have the power to demand answers from Trump’s biggest lender, Deutsche Bank. She has called Trump an immoral “scumbag” and was a target of the pipe bombing campaign that singled out Trump critics.

Jerry Nadler

The incoming chairman of the House judiciary committee will have a major role in any possible future impeachment proceedings, if Trump is accused of having broken the law, conspired with the Kremlin or obstructed justice by special prosecutor Robert Mueller. New York congressman Nadler wants to investigate whether Brett Kavanaugh, the supreme court justice, lied under oath during confirmation hearings.

Elijah Cummings

The incoming chairman of the House oversight committee has many issues he wants to investigate, including whether Trump has improperly enriched himself in office. Cummings said he wants to investigate whether the administration has illegally profited from foreign leaders staying at the Trump hotel. Cummings is also seeking to investigate voting rights and the disenfranchisement of minority voters.

Adam Schiff

The California Democrat and new likely chairman of the House intelligence committee has been the most vocal Democratic critic of Trump’s alleged ties to Russia and its handling of the Russia investigation. Schiff wants to pursue whether Trump has any financial obligations in Russia, which could compromise the president. Hours after the Democratic House victory, he wouldn’t rule out calling Trump’s son, Donald Trump Jr, to testify before a public hearing.