The Monastery of Iveron (“Iberian” or Georgian) is on the northeast coast of the peninsula of Mount Athos, approximately 4 km from Karyes. Until between 1010 and 1020 Iveron was called the "Monastery of the Iberian" or "of Euthymios"; thereafter it was called the "Lavra of the Iberians." The first Georgians to come to Athos were John the Iberian and his son Euthymios the Iberian, who entered the Great Lavra of Athanasios in the 960s before moving to nearby kellia. In 979/80 the ascetic/general John Tornikios, after winning a battle over the rebel Bardas Skleros and amassing vast amounts of booty, returned to Athos to found a new lavra for Iberians at the site of the monastery "ton Kiementos." At this time Tornikios received the Kolobou Monastery from Empire Basil II.

Under the first hegoumenoi - John the Iberian (980-1005), Euthymios (1005-1019), and Euthymios's cousin George (1019-29)—a scriptorium was established for the translation of Greek religious texts into Georgian and the copying of Greek and Georgian manuscripts. Thereafter Iveron continued to be an important center of Byzantine-Georgian cultural interaction and the dissemination of texts in Georgian. The number of monks at the monastery reportedly grew to 300, and Iveron initially owned more land than Lavra. In addition to extensive properties on Athos, Iveron had possessions in Chalkidike, the Strymon valley, and Thessaloniki.

Throughout the Byzantine period there was rivalry at Iveron between the community of Greek monks, who were in the majority, and the Georgians; the two groups celebrated the liturgy separately. The Georgians were in authority in the early period, and held their services in the katholikon, even though they were outnumbered. In the 14th century, however, the Greeks gained dominance at Iveron; an act of 1356, noting that the Greek monks were "more numerous and capable," stated that the hegoumenos was to be Greek and that the Greeks were entitled to hold their services in the principal church.

The archives contain over 150 documents of Byzantine date. Those published to date (the earliest is of 927) deal primarily with sales and donations of property; they provide valuable information on the topography and prosopography of Macedonia. The will of Kale Pakouriane (of 1090) contains a long list of liturgical vessels and textiles given to the monastery. Iveron's library preserves a major collection of 337 Byzantine manuscripts, in addition to 86 Georgian manuscripts, including unique hagiographical codices. The most important Byzantine books are a lavishly illustrated 12th-century copy of Barlaam and Ioasaph and the 13th-century Gospel book. The katholikon, which has undergone numerous restorations and modifications, was originally built in 980-83 and is one of the oldest surviving Christian structures on Athos. Dedicated to the Virgin, it is a cross-in-square church, with side chapels added later. Its pavement probably dates to the mid-11th  century.