The Western Wall is not a remnant of the Temple itself, and one of its most familiar customs is something visitors do rather than something built into the stone.
A retaining wall, not the Temple
The wall is a surviving section of the massive retaining structure Herod the Great built in the first century BCE to expand and support the platform of the Second Temple, not a wall of the Temple building itself, which stood elsewhere on the platform above and was destroyed in 70 CE. Wilson's Arch, a still-standing section of an ancient bridge, extends the accessible prayer area underground, and excavated tunnels running the wall's full length reveal that only a fraction of the original structure is visible at street level.
Notes left in the cracks
Visitors have long placed small folded paper notes bearing personal prayers into gaps between the wall's stones, a practice with no fixed origin date but widely observed today regardless of a visitor's religious background. Periodically the accumulated notes are cleared and given a respectful burial, in keeping with Jewish practice for disposing of writings that reference the divine.
Under excavation as much as under prayer
Ongoing archaeological work along the wall's base and in adjoining tunnels continues to reveal new sections and Herodian-era construction details, meaning the wall's known physical extent has kept expanding well after the site's basic religious significance was already fixed.