The Kaliver Dynasty began with Rabbi Yitzchak Isaac Taub (1744-1821) of Nagykálló (in Yiddish Kaliv, Kalov, Kalev), Hungary. He was the first Hassidic Rebbe in Hungary. He was discovered by Rabbi Leib Sarah's, a disciple of the Baal Shem Tov. Rabbi Leib first met Rabbi Isaac when he was a small child, a small shepherd boy. Rabbi Leib told his mother, a widow, that her son was destined to be a great Tzaddik. He took the small child to Nikolsburg to learn with Rabbi Shmelke of Nikolsburg. Rabbi Isaac grew to be a great rebbe and was known as "the Sweet Singer of Israel". He composed many popular Hasidic melodies. Often he adapted Hungarian folk songs, adding Jewish words. He taught that the tunes he heard were really from the Holy Temple in Jerusalem, and were lost among the nations over the years, and he found them and returned them to the Jewish people. He said that the proof that it was true was that the gentile who would teach him the song would forget it as soon as the rebbe learned it. He was famous for composing the traditional Hungarian Hasidic tune "Szól a kakas már".
Today there are two Kaliver Rebbes. They are distinguished by the spelling of their title. The rebbe in Jerusalem is called the Kaliver Rebbe, . The rebbe in New York is the Kalover Rebbe, .