See title.
From 70 AD to 130 AD it was a burnt out shell of Herod's temple.
In 130 AD Hadrian constructed a temple to Jupiter on the spot.
In 363 AD Julian allowed the Jews to build a temple on the temple mount but work only lasted a short time before an earthquake caused the work to stop.
Sometime after 363 there seems to have been a Christian church of some kind built on the site.
In 610 AD the Jews began clearing away the Christian church to rebuild the temple. This lasted about 5 years before control of Jerusalem was given back to Christians who tore down the work done by the Jews.
In 637 Caliph Omar built the first Muslim Mosque on the site.