The influence of the Vilna "Ga'on" in emphasizing Talmudic learning as the key component of Judaism was transmitted to future generations through the influence of his students.
Rabbi Hayyim and the Great Yeshivah of Volozhin
In 1803, Rabbi Chaim ben Isaac of Volozhin (1749-1821) established what was to become the classic model of Lithuanian yeshiva, a central institution that was designed not merely to educate local youths, but primarily to serve as a focus for the finest students throughout the Jewish world. At the "Etz Hayyim" ("Tree of Life") yeshivah the students would be exposed to a demanding schedule, extending for six days a week. Studies often continued from 3:00 a.m. to midnight, with brief interruptions for prayer and meals. The content of the curriculum emphasized a rigorously logical analysis of the Talmud.
The graduates were not usually expected to become professional Rabbis (students who were suspected of studying the Rabbinic curriculum were frequently looked down upon), but to return to their communities and apply their strong grounding in Judaism to daily pursuits.
Rabbi Hayyim's approach exerted a decisive influence on the curriculum of the Lithuanian Yeshivot.
After 1879 the yeshivah was in a constant struggle with the Czarist government, who closed the institution several times on account of its refusal to include secular subjects in its curriculum. The institution that was refounded in 1899 did not retain its earlier preeminence.
Rabbi Naphtali Zvi Judah Berlin (1817-11893)
Rabbi Naphtali was known by his acronym as the "Netziv" of Volozhin. He was the son-in-law of Rabbi Isaac, son and successor to Rabbi Hayyim of Volozhin, and he became the head of the yeshivah in 1854. He remained at the head of that institution for some forty years, strengthening it and expanding its student body.
While sharing the yeshivah's tradition of precise logical analysis, he made a special contribution in his broadening of the curriculum to include the entire Babylonian Talmud, and in his commentaries to early Rabbinic texts like the Sifré and the She'iltot.
Rabbi Hayyim Soloveitchik of Brisk (1853-1918)
Rabbi Hayyim "Brisker" was born in Volozhin and spent much of his life studying there. Developed an analytical approach to Talmud study, emphasizing its logical and conceptual features, and demonstrating how disputes in the Talmud and its commentators derive from these conceptual distinctions. The "Brisker" mode of study rejected the extreme logical hairsplitting that was cultivated in many yeshivahs.
In 1892, following the closing of the Volozhin yeshivah, Rabbi Hayyim moved to Brisk (Brest-Litovsk) where he soon succeeded his father as the community Rabbi, devoting his energies unselfishly to communal concerns.
Following the outbreak of World War I and the German invasion of Lithuania in 1915, most of the important yeshivot were forced into exiles to the eastern domains of Russia and the Ukraine, a fact which resulted in the expansion of their influence to areas previously remote from intensive Jewish learning.
Sources: Prof. Eliezer Siegel's Home Page