By Rurikovichi historians mean the first dynasty of Russian princes and kings. They didn't have a surname, and the dynasty received its name by the name of its legendary founder - Novgorod prince Rurik, died in 879 year.
Grand duke of Kiev Igor (who is considered to be the son of Rurik in the annals) is, however, more authentic historical person and the ancestor of the dynasty.
Dynasty of Rurikovichi was at the head of the Russian state over 700 years. Rurikovichi ruled the Kiev Russia, and then when it fell, in XII century, into large and fine Russian princedoms. Great Princes of Moscow from the dynasty also were at the head of the state after unity of all Russian lands around Moscow. Descendants of former princes lost their estates and made the supreme layer of Russian aristocracy, however they kept title "prince".
In 1547 Grand duke of Moscow accepted title "King of all Russia". The last representative of Rurikovichi dynasty on Russian throne was king Fedor Ivanovich, who died childless in 1598. But it does not mean, that Rurikovichi dynasty finished also - only its youngest branch in Moscow. And the man's posterity of other Rurikovichi (former apanage princes) by then got surnames: Baryatinskie, Volkonskie, Gorchakovy, Dolgorukovy, Obolenskie, Odoevskie, Repniny, Shuiskie, Sherbatovy etc.
All Rurikovichi that ruled Russia are hard to remember - too much of them. But to know the most famous ones is necessary. Among Rurikovichi the largest statesmen were: Great Dukes Vladimir the Sacred, Yaroslav the Wise, Vladimir Monomakh, Yury Dolgoruky, Andrey Bogolyubsky, Всеволод the Big Nest, Alexander Nevsky, Ivan Kalita, Dmitry Donskoy, Ivan the Third, Vasily the Third, King Ivan the Terrible