Matt Rourke/AP
The sign at the office of House Speaker Kevin McCarthy of California is installed on Capitol Hill in Washington, early Saturday, January 7, 2023.
CNN  — 

Now that a House speaker has been selected following a dayslong stalemate and members have finally been sworn in, the chamber can look toward picking back up business and organizing GOP-led committees.

Every new Congress must pass a new set of House rules, and doing so will be the top of the 118th Congress’ to-do list when the House reconvenes Monday.

With House Republicans’ majority, comes a newfound power to set the agenda – investigative and legislative.

Here’s a look at what Republicans plan to do with their new House majority:

Legislative agenda

House Republicans will be limited in their ability to pass bills through Congress with Democrats in control of the Senate and the White House – where the president can exercise veto power over legislation. Still, House Republicans will be able to push messaging bills that highlight their agenda.

In an exclusive, wide-ranging interview with CNN ahead of the 2022 midterm elections, then-House Minority Leader Kevin McCarthy outlined his plans for power. Those plans include tackling inflation, rising crime and border security, and he left the door open to launching eventual impeachment proceedings, which some of his members have already begun to call for.

There will also be some must-pass policy issues – like funding the government – that will test the ability of Republicans and Democrats to work together.

Investigative agenda

With subpoena power and control over powerful committees, the House GOP plans to make investigations into the Biden administration a top priority. Among its targets are:

Hunter Biden. GOP Rep. James Comer, who is in line to chair the House Oversight Committee, said that “in the 118th Congress, this committee will evaluate the status of Joe Biden’s relationship with his family’s foreign partners and whether he is a President who is compromised or swayed by foreign dollars and influence.”

The heart of Comer’s investigation will be digging into more than 100 suspicious activity reports that Republicans claim banks have filed related to the president’s son Hunter Biden’s financial activities. Comer has said, “We would love to talk to people in the Biden family, specifically Hunter and Joe Biden.”

The White House said the investigations are politically motivated and a waste of time. Such reports are not conclusive and do not necessarily indicate wrongdoing.

The Department of Justice and FBI. GOP Rep. Jim Jordan, who is widely expected to chair the House Judiciary Committee, sent a letter to Attorney General Merrick Garland in November requesting a slew of documents on everything from the Justice Department’s alleged “targeting” of Project Veritas to the FBI search for classified documents at former President Donald Trump’s Mar-a-Lago resort.

The southern border. After winning the majority, Republican members of the House Judiciary Committee sent a letter to Department of Homeland Security Secretary Alejandro Mayorkas telling him and other department officials to be prepared to testify.

The Afghanistan withdrawal. Biden’s decision to remove US troops from Afghanistan in 2021 led to a frantic attempt by many Afghans to flee the county, with devastating scenes of people clinging to the wings of planes as they tried to escape before the Taliban government officially assumed power. Republicans have signaled that they are eyeing potential probes into the events.

Covid-19 origins. Rep. Cathy McMorris Rodgers, the top Republican on the Energy and Commerce panel, has said that “how the pandemic started, that’s probably the most important public health question that needs to be answered.” Two studies released last year both concluded that a seafood market in Wuhan, China, was most likely the epicenter for the virus.