The most high-profile race is in Utah's 4th congressional district, where Democratic Rep. Jim Matheson squared off against Republican Mia Love.
They traded leads on election night before Matheson declared a narrow victory. Love conceded shortly thereafter, but she's holding out some hope that uncounted mail and provisional ballots could turn the results.
Matheson is leading by only 2,646 votes. Canvassing boards in Salt Lake, Utah, Sanpete and Juab counties are adding thousands of uncounted paper ballots to the mix there.
Final election results for most races should be known late Tuesday.