Currently, with 53 seats, the Republicans occupy a majority of the 100 seats in the Senate (Senate.gov).
The 2020 United States Senate elections will be held on November 3, 2020, with the 33 Class 2 seats of the Senate being contested in regular elections.
According to Vox's Dylan Matthews, the Republican stronghold can be upset:
There’s a chance, if literally everything breaks in Democrats’ favor, that they retake the Senate. But it requires a lot going right for them, and even one botched race means Republicans hold control.
On paper this should have been a promising year for Dems. Twenty-three Republican seats are up, compared to only 12 Democratic seats; these were, except for a couple of special elections, seats that were last open in 2014, when Republicans gained a whopping nine seats. You would think that Democrats could regain some of those nine that they lost, but you’d mostly be wrong. Democrats lost seats in Alaska, Arkansas, Louisiana, South Dakota, and West Virginia that they’re basically not contesting this time around. Iowa and Montana look only slightly better.
Instead, Democrats’ hopes rest on the two 2014 losses they think they can reverse — in North Carolina and Colorado — as well as a special election in Arizona, an unlikely Alabama seat they won in 2017, and Susan Collins’ once-safe seat in Maine that they’re hoping her vote for Kavanaugh will make competitive. Sweeps of this magnitude do happen (2006 and 2008 both saw huge Democratic sweeps), they’re rare, especially as the parties have polarized geographically, and Democrats are underdogs in Alabama and North Carolina in particular. There’s a chance the Dems pull it out, but I think it’s quite unlikely.
Will the GOP hold the Senate in 2020?
This resolves positively if the Senate Majority leader elected at the start of the 2021 congressional session is a Republican.