How did the walls of Constantinople hold off enemies for centuries?

They held because they were built in layers, so that an attacker had to win several fights before reaching the city, and because each side of the city had its own defence. The famous double line of the Theodosian walls was built in the 5th century, and when well manned the walls were almost impregnable for any medieval besieger. They saved the city, and the empire with it, during sieges by an Avar-Sassanian coalition, Arabs, Rus' and Bulgars, among others.

Start with the land side. The first phase was built while the emperor Theodosius II was still a boy, under the direction of Anthemius, the praetorian prefect, and finished in 413. The inner wall was a solid structure 4.5 to 6 metres thick and 12 metres high, with a lower outer wall in front of it across a terrace. Beyond that ran a moat more than 20 metres wide and up to 10 metres deep, with a low crenellated wall on its inner side as a first line of defence.

Then came the sea. A heavy chain or boom, installed by Emperor Leo III, supported by floating barrels, stretched across the mouth of the Golden Horn to keep enemy ships out. On the other coast, strong currents made an attack by a fleet almost impossible.

Repair was part of the defence. In 447 an especially powerful earthquake destroyed large parts of the wall, including 57 towers. With Attila the Hun threatening in the Balkans, the walls were restored in a record 60 days, using the city's chariot-racing factions as workers.

But walls are only as good as the people on them. In 1204 a first attack by the Crusaders failed, but a second from the Golden Horn succeeded. In 1453, gunpowder cannons played a part in the fall to the Ottomans but never breached the walls themselves; the defenders were too few to hold both lines of wall.