In fact, Karaism, the Jewish movement which is well-known due to its emphasis on biblical literalism, is rarely considered fundamentalist.
Religious Zionism is more associated with political extremism while Haredi Judaism is associated with men studying torah every day and making sure all actions are in line with the will of Hashem.
It primarily began with the teachings of Rabbi Abraham Isaac Kook (1865–1935), who saw Zionism as a part of a divine scheme to return Jews to their ancestral homeland and eventually bring about the coming of the Messiah.
Religious Zionism gained a new momentum after the Six-Day War in 1967, when Israel conquered the West Bank, a territory which is rich in Biblical history.
The Gush Emunim movement took off under the leadership of Zvi Yehuda Kook and it also spearheaded the proliferation of Israeli settlements in the newly conquered territory.