The official presiding officer of the U.S. Senate is the vice president, but a president pro tempore is elected to fulfill the duties when the vice president is not in attendance. The vice president normally does not preside unless he needs to cast the deciding vote on an issue.
The president pro tempore is elected from the majority party in the Senate. Currently the vice president and presiding officer is Mike Pence, and the president pro tempore is Senator Orrin Hatch. According to the United States Senate website, the presiding officer "is charged with maintaining order and decorum, recognizing members to speak, and interpreting the Senate's rules, practices and precedents."