The Italian Borgia families we're incredibly influential in Catholic/Papal politics. As a lay-historian, I can't necessarily find any modern branches of the family that are still active. Did the family die out during the Renaissance or did they "rebrand" and marry into other Italian families as a way to hide their influence in the Middle ages?
They are still around. There are two main branches.
Branch one is the Borgia/Borja Dukes of Gandia. The current leader of this branch is Duchess Angela Maria Tellez-Giron y Duque de Estrada. They are Spanish aristocrats. Part of this branch is descended from Saint Francis Borgia, a Jesuit who was canonized in 1670. The most famous modern member is Rodrigo Borja Cevallos, who was the President of Ecuador from 1989 - 1992.
The second branch is the Borgia Borbon-Busset branch that includes the Borbon Parma family. Carlos, Duke of Parma is the leader of this branch. There is a minority of people who believe that this branch are.the true heirs to the Spanish throne.