After Timur's death in 1405, Samarkand became a centre of science and art under his grandson Ulugh Beg, who was both ruler and astronomer; the star catalogue prepared at his observatory has an accuracy unmatched in the West until Tycho Brahe. The madrasa completed in 1420 is the square's first building and an institution where mathematics and astronomy were taught.

The square as it stands came together from three buildings: the Ulugh Beg Madrasa (1420), the Sher-Dor Madrasa facing it (1636) and the Tilla-Kari madrasa and mosque between them (1660). Sher-Dor repeats the façade of the first almost as a mirror — across two centuries, the measure, proportion and colour were held. This is the product of an urban tradition rather than a single architect.

The architectural language is the Timurid synthesis: a vast pointed iwan (pishtaq), minarets at the corners, double-shelled onion domes and turquoise and lapis tile mosaic covering every surface. The lion-tiger figures carrying the sun on their backs on the Sher-Dor façade are a rare but real instance of figural depiction in Islamic architecture, readable as the survival of a motif from pre-Zoroastrian Iranian iconography. The square itself matters too: the iwans facing one another produce an enclosed, defined public space — an urban solution contemporary with the squares of the Italian Renaissance and independent of them. It underwent major restoration in the Soviet period and is on the UNESCO World Heritage list today.