Zaydi Shia affirm that the rightful Imam must be a learned and pious descendant of Ali and Fatima, through either Hasan or Husayn, who publicly claims the office and rises in arms to establish just rule. Unlike the Twelver and Ismaili lines, which pass the imamate by explicit designation from father to son, Zaydism makes the office contingent on a qualified claimant actually asserting it, so that the imamate can lapse when no one rises and be revived when one does.
The Yemeni Zaydi imamate proper was founded in 897 CE by al-Hadi ila'l-Haqq Yahya, who established his rule at Sada in the northern highlands and whose teaching developed into the Hadawi school of law that Zaydis follow; in jurisprudence this school stands closer in method to Sunni fiqh, drawing on reasoning and analogy in ways the Twelver Shia legal tradition, built instead around the rulings of the Twelve Imams, does not.
The Zaydi imamate in Yemen endured, with interruptions, for over a thousand years until the republican revolution of 1962 overthrew the last ruling imam, Muhammad al-Badr, an event that ended Zaydi imamate rule as a state even as Zaydi religious identity and the Hadawi legal tradition continued, including within the modern Houthi movement, which has drawn on Zaydi revivalist ideas since the 1990s.