The Genpei War
The Taira and the Minamoto fought the Genpei War from 1180. It ended in 1185 with the destruction of the Taira at the sea battle of Dan-no-ura, where the child emperor Antoku, a Taira grandson, was drowned.
Yoritomo
The victor, Minamoto no Yoritomo, did not move to Kyoto. He governed from his own base at Kamakura, far to the east, and in 1192 the court named him sei-i taishōgun. Now the title belonged to the man who actually ruled the country, and it no longer lapsed.
Many historians date his government from 1185 instead, when he won the right to appoint his own men as stewards and constables in the provinces. Either way, Japan now had two centres: the emperor’s court in Kyoto, which kept its ceremonies and titles, and the shogun’s government in Kamakura, which kept the peace and the land.
The Hōjō regents
Power soon slipped one step further from the throne. After Yoritomo died in 1199 and his two sons were gone, the shoguns were boys brought from the Fujiwara and then imperial princes, while the family of Yoritomo’s widow, the Hōjō, governed in their name as regents, shikken.
So the emperor had a shogun, and the shogun had a regent, and it was the regent who ruled. There were nine Kamakura shoguns in all.
The Mongols
It was the Hōjō regency that met the Mongol invasions of 1274 and 1281, sent by Kublai Khan. Both were beaten back, with the help of storms later remembered as kamikaze, the divine wind.
Victory brought no spoils to share out, and the warriors who had fought expected reward. The cost of the wars weakened the Hōjō. In 1333 Emperor Go-Daigo rose against them, Kamakura fell, and for three years he tried to govern in person, a period known as the Kenmu Restoration.