The narrative core is the Battle of Uhud in 625 CE. In the accounts preserved in the early biographies and hadith, Ali's sword broke in the fighting, and the Prophet handed him a sword, taken among the spoils, that came to be called Zulfiqar. The name is generally understood to mean "the one with notches (fiqar)," perhaps from grooves or fluting along the blade; it has also been linked to a word for the spine, and later imagination reshaped it into a blade that splits into two points.
Ali's feats made the sword proverbial. The couplet "la fata illa Ali, la sayf illa Dhu al-Fiqar" spread across the Islamic world and was inscribed on weapons, standards and monuments; the bifurcated Zulfiqar became a heraldic device on Ottoman and other banners and a common motif in popular and devotional art. In Shia tradition the sword is handed down as an attribute of the Imams and gathers further legendary associations, including traditions tracing its origin to the beginning of the world.
Physically, the sword cannot be followed. Unlike the swords at Topkapi, which are objects with a custody history however traditional, Zulfiqar is not represented by any single agreed artefact; where later swords are named for it, this is homage or attribution rather than an unbroken provenance. Its life is in memory, art and devotion rather than in a museum case.