"The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided" (U.S. Constitution, Article I, section 3). Since 1789, 272 tie-breaking votes have been cast.
The vice president presides over the Senate only on ceremonial occasions or when a tie-breaking vote may be needed. When the vice president is absent, the president pro tempore presides over the Senate.