In 1180, Prince Mochihito appealled to the Minamoto family throughout Japan to rise up against Taira no Kiyomori and the Taira family that had usurped the power of the emperor. Yoritomo, based in Kamakura, and his cousins based throughout Japan raised armies to begin the Genpei War.
Liquidating his rival cousins and finally defeating the Taira at the Battle of Dan-no-ura in 1185, Yoritomo established the supremacy of the warrior samuraicaste and the first bakufu at Kamakura, beginning the feudal age in Japan which lasted until the mid 19th century.
Yoritomo was granted the title of shogun in 1192, which was eventually passed to his oldest son Yoriie in 1202.
Minamoto no Yoritomo was the third oldest son of Minamoto no Yoshitomo, the heir of the Minamoto (Seiwa Genji) clan, and his official wife, Fujiwara no Saneori, who was a member of the illustrious Fujiwara clan.
As for Yoritomo, the new head of the Minamoto, he was exiled to Hirugashima, an island in Izu province (on the Kanto Plain), which at that time was under the rule of the Hōjō clan.
Yoritomo was defeated at Ishibashiyama in his first major battle, but in the end he triumphed over his rival cousins, who sought to steal from him control of the clan, and over the Taira, who suffered a terrible defeat at the Battle of Dan-no-ura in 1185.