The Zaidi school of thought represents a middle ground between traditional sunnism and 12 imamer shi-itism.
Zaidis believe that any descendant of the Prophet can be the imam, as long as they meet certain criteria. They reject the notion of the "hidden imam".
Theologically, Zaidism is a rationalist school of thought, it adheres to the rationalist doctrine known as mu'tazili. This doctrine is opposed to the wahabbi/salafi tendencies of (a) anthropomorphism in Qur'an interpretation, and (b) fatalism in the free will debate. The Qur'an interpreter Zamakhshari is an example of a mu'tazili scholar.
The Zaidi school flourished in Yemen for 1,000 years. It was begun there by Imam al Haadi, a descendant of Hassan bin Ali. Before that, it originated in Arabia with Zaid bin Ali bin Hussain bin Ali, one of the teachers of Abu Hanifa.
To read "A Quick Introduction to Zaidiya" (Zaidiya is the Arabic word for Zaidism) written by a Zaidi, click on the following link: