They were generally accepted as the spiritual leaders of the Jewish community worldwide in the early medieval era, in contrast to the Resh Galuta (exilarch) who wielded secular authority over the Jews in Islamic lands.
The Sura Academy was originally dominant, but its authority waned towards the end of the Geonic period and the Pumbedita Gaonate gained ascendancy (Louis Ginzberg in Geonica).
The Geonim officiated, in the last place, as directors of the academies, continuing as such the educational activity of the Amoraim and Saboraim.
Despite the difficulties which hampered the irregular communications of the period, Jews who lived even in most distant countries sent their inquiries concerning religion and law to these officials in Babylonia.
Gaon Ẓemaḥ refers in a responsum to "the ancient scholars of the first row, who take the place of the great sanhedrin".
The questions were usually limited to one or more specific cases, while the responsum to such a query gave a ruling, a concise reason for it, together with supporting citations from the Talmud, and often a refutation of any possible objection.
The later geonim did not restrict themselves to the Mishnah and Talmud, but used the decisions and responsa of their predecessors, whose sayings and traditions were generally regarded as authoritative.
These responsa of the later geonim were often essays on Talmudic themes, and since a single letter often answered many questions, it frequently became book-length in size.
Discussions followed, and difficult passages were laid before the gaon, who also took a prominent part in the debates, and freely reproved any member of the college who was not up to the standard of scholarship.
At the end of the yarchei kallah the gaon designated the Talmudic treatise which the members of the assembly were obliged to study in the months intervening until the next gathering took place.
A large number of the geonic responsa originated in this way; but many of them were written by the respective Geonim without consulting the kallah assemblies convened in the spring.