As they left and went down the mountain, they
asked Jesus about Elijah.

From Malachi 4:5-6 they expected Elijah to re-
appear on earth before the Messiah came, and
work a mighty change preparing Israel for the
Lord:

"Behold, I will send you Elijah the prophet
before the coming of the great and dreadful
day of the Lord: And he shall turn the heart
of the fathers to the children, and the heart
of the children to their fathers, lest I come and
smite the earth with a curse"