January 12, 2021 12:02 PM EST

The electoral victories of Democrats Raphael Warnock and Jon Ossoff in Georgia last week will result in a 50-50 split between Democrats and Republicans in the U.S. Senate—a rare event; it’s only the fourth time the Senate has been evenly divided.

Because the Constitution designates the vice president as the president of the Senate, Vice President-elect Kamala Harris will hold the tie-breaking vote and all simple majority, party-line stand-offs will likely break for Democrats. That means Warnock’s and Ossoff’s wins open up a host of possibilities for what Democrats may be able to accomplish under the Biden Administration.

But the Democrats holding the narrowest possible majority leaves some major obstacles and mine fields for the party. The Senate cloture rule, for example, requires 60 members to end debate and vote on most topics, which, in practice, will allow Republican Senators to filibuster much of the Democrats’ legislative agenda.

Here’s how the 50-50 split is likely to work in real life.

The first hurdle is the organizing resolution

Incoming Democratic Majority Leader Sen. Chuck Schumer and outgoing Republican Majority Leader Mitch McConnell will have to agree on a set of rules, known as an organizing resolution, which governs how the Senate works. The organizing resolution determines everything from committee membership and staff budgets, to who gets the best office space.

Even with Harris’s tie-breaking vote, Schumer will need McConnell’s support: passing the organizing resolution requires 60 votes. As a result, Republicans will likely end up with much more power than a minority would usually hold.

The last time the Senate was split 50-50, in 2001, lawmakers agreed on an organizing resolution that allowed both parties to share power. Under that deal, the parties agreed to split committee memberships and staff equally and changed the rules, making it so that if a tie vote prevented a measure from moving out of committee, either the majority or the minority leader could bring the bill to the Senate floor.

Schumer and McConnell may take a cue from that 2001 agreement, but Senate observers note that, in these hyper-partisan times, agreeing on even the rules of the road may be tricky. “As partisan as it was in 2000, things have become even more partisan,” says Sarah Binder, a senior fellow in governance studies at the Brookings Institution.

The prospect of ditching the filibuster

In theory, Senate Democrats could change the cloture rule—and, with it, the need for 60 votes. They could, in other words, kill the filibuster.

There are two ways that Democrats could do that. The first is by holding a vote to change the Senate’s standing rules. The only problem is that a vote to change the rules requires a two-thirds majority. So, as has happened many times in the past, Senators can simply filibuster the attempt to eliminate the filibuster.

The second way to kill the filibuster is known as the “nuclear option.” That would mean that Senate Democrats vote to establish a new precedent in the chamber, which can require only a simple majority: the 50 Democrats plus Harris. The nuclear option has been employed twice in the past decade—once in 2013 by Democratic Senate Majority Leader Harry Reid and then once in 2017 by McConnell—to make it easier to confirm executive and judicial nominations.

In recent months, Democrats have been clamoring to eliminate the filibuster. Former President Barack Obama called it a “Jim Crow relic” and President-elect Biden said he’d consider eliminating it, depending “on how obstreperous [Republicans] become.” But Democrats are hardly in lock step over the issue. Sen. Joe Manchin of West Virginia has has said he will not support such a vote.

If the filibuster stays, what can Democrats do?

Because so much legislative action can be thwarted by a filibuster—or simply by losing the support of one or two moderate Democrats—the party’s slim majority will likely limit its ability to pass ambitious legislation. “It gives sort of a fighting chance to make a down payment on some of those agenda items,” Binder says. “But it’s not sufficient in any way to really empower Democrats to do a lot of big stuff.”

Depending on the issue, Democrats have some options. If a seat opens up on the Supreme Court, for example, Democrats could confirm a new justice with no Republican support. Democrats could also use the Congressional Review Act, which also requires just 51 votes, to unwind some of President Donald Trump’s last-minute regulations.

Democrats also have access to a limited budget tool known as “reconciliation,” which can be used to pass legislation related to the budget or spending, and requires only 51 votes. In 2001, the Republicans used the tool to pass the George W. Bush-era tax cuts, and in 2017, they tried to use it to repeal the Affordable Care Act. This year, Democrats could use it to pass a larger coronavirus relief package, expand the Affordable Care Act, or pass some of Biden’s proposed climate plans—so long as the bills retain support from all 50 Democrats, including moderates, like Manchin or Sen. Kyrsten Sinema of Arizona.

But reconciliation is not a get-out-of-jail-free card. The process can only be used once a year on a spending bill and can’t be used for just any spending. For instance, it can’t be used to touch Social Security, increase the deficit beyond a 10-year window or touch on topics outside a committee’s jurisdiction.

Who controls the Senate for now?

Republicans have the majority until Inauguration Day.

Georgia counties have until Jan. 15 to officially certify the results of Warnock’s and Ossoff’s elections, and Georgia Secretary of State Brad Raffensperger has until Jan. 22 to make the victories official. (Though the process could progress more quickly). Once Warnock and Ossoff have an official certificate of election, they will be sworn into office.

Until Inauguration Day, Vice President Mike Pence will preside over the chamber. After Jan. 20, Kamala Harris will have the honors.

Write to Abigail Abrams at abigail.abrams@time.com.

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