This year, as in every even-numbered year, about a third of U.S. Senate seats will be up for election. Given the 50-50 split in the Senate between Democrats and Republicans, each of those races has the potential to tip the chamber's balance of power one way or the other. But elections aren't the only way that can happen.
In the event that a sitting senator resigns or dies, or the position otherwise becomes vacant, governors in 46 states have the power to appoint a temporary replacement. And in most of those states, governors have free rein to appoint whomever they wish, with the appointee serving until a successor is elected to fill out the rest of the term. The evenly split Senate means that even a single governor could, hypothetically, determine which party controls the chamber.