Per Mark Warner, the committee's top Democrat, elements of the bill include:

The FBI would be required to receive an after-the-fact review from the national security-focused FISA court when they used the surveillance program in some cases.

Warner said that "if the court determined that some agent inappropriately used that, that information could not be used in any further proceeding."

The program would be renewed for a total of 8 years.

The FISA court would have to approve the revival of the program's so-called "about" searches that were previously halted and have been a target of criticism by privacy advocates. Congress could stop those queries from being brought back, per Warner.

What's next?: The bill has yet to move to the Senate floor. There are also differences between the reform bill in the House and what Warner described: the House bill only reauthorizes the program for six years, for example.

Go deeper: New York Times reporter Charlie Savage has been keeping tabs on the differences between some of the reauthorization proposals.