The revolt that began in 66 was as much a civil war as a war against Rome. Factions inside Jerusalem fought each other through the siege, burned each other's grain stores, and were still fighting when the walls were breached. Titus took the city in the summer of 70, and the temple burned. Whether the fire was ordered is disputed in the sources themselves: Josephus says Titus wished to spare the building, which is exactly what a historian writing under Titus's family would say.
The loss was not only of a building. The temple was the only lawful place of sacrifice, the seat of the priesthood, the destination of pilgrimage three times a year, the treasury and the effective centre of Jewish public life. Its destruction ended the sacrificial system at a stroke and left the priesthood without a function. The Arch of Titus in Rome still shows the menorah and the temple vessels carried in triumph.
The rabbinic tradition remembers the period through Yohanan ben Zakkai, who is said to have been carried out of the besieged city and to have obtained from the Roman commander permission to establish a school at Yavneh. The story is told in several versions with different details, which is a sign of legend, but the institution at Yavneh was real and the shift it represents, from temple to study house, is the central fact of what followed.