Hagia Sophia's dome seems rendered weightless by the unbroken arcade of arched windows under it, which help flood the colourful interior with light. The dome is carried on pendentives—four concave triangular sections of masonry which solve the problem of setting the circular base of a dome on a rectangular base. At Hagia Sophia the weight of the dome passes through the pendentives to four massive piers at the corners. Between them the dome seems to float upon four great arches.
At the western (entrance) and eastern (liturgical) ends, the arched openings are extended by half domes carried on smaller semidomed exedras. Thus a hierarchy of dome-headed elements builds up to create a vast oblong interior crowned by the main dome, a sequence unexampled in antiquity.
The structure has been severely damaged several times by earthquakes. The dome collapsed after an earthquake in 558; its replacement fell in 563. There were additional partial collapses in 989 after which an Armenian architect named Trdat was commissioned to repair the damage and again 1346. In the era of Süleyman the Magnificent, Mimar Sinan (Sinan the Architect) built extra attachments to prevent it from collapsing.
All interior surfaces are sheathed with polychrome marbles, green and white with purple porphyry and gold mosaics, encrusted upon the brick. On the exterior, simple stuccoed walls reveal the clarity of massed vaults and domes. (Wikipedia)
You can watch this 10 minute video excerpt from:
Paradise Found: Islamic Architecture & Art
for more information about the Aya Sophia, and other great mosques and palaces in Istanbul.