Answer:
   
   Jewish tradition has no role for the parents. In the west, we tend to
   have them walk their children down the aisle, but even having an aisle
   is a western culture thing, not a Jewish one. And the rabbi doesn't
   marry them. Marriage requires the couple and witnesses. The rabbi is
   there as "mesadeir qiddushin" (arranger of the marriage), he's there
   to insure that everyone does everything correctly.
   
   Note that one can also honor a second rabbi with reading the kesuvah,
   and six other rabbis to read the blessings. The cantor chants/sings
   the traditional greetings and often a song about Jerusalem before the
   groom breaks the glass. The couple also often honors three sets of
   winesses, having one group witness the tana'im (the contract
   specifying which family will pay for what of the wedding), one for the
   kesuvah, and one pair guarding the door to the yichud room.

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