The Kakuyids established a series of villages and reinforced the network of qanats around Yazd. Hence greatly contributing to the rapid urbanization of the region in the eleventh century. Yazd under the subsequent rule of the Atabegs survived the Mongol invasion of Persia in 1220 to later become a refuge for Islamic culture and learning. The Il-Khanid rule under Sayyid Rukn al Din in the fourteenth century witnessed an increase in construction with the use of the waqf as an instrument for urban development. The Muzaffarid conquest in 1313 ushered in an era of prosperity and development as Yazd became capital to the provinces of Kerman, Fars and Shiraz. 

Large urban design projects were initiated and the city walls were rebuilt in 1346-7, nearly doubling the size of the city. The complex of Vaqt va Sat comprising of a shrine, library, college and observatory was constructed next to the Atabeg Friday mosque, which was itself reconstructed half a century later in 1375.The Timurid conquest reinforced Yazd's status as an important military stronghold in central Iran when defense walls and fortifications were added to the city's southern limits in 1395. Yazd became a center of religious education under the reign of the Timurid governor, Amir Chaqmaq. Yazd passed into Safavid control in the early sixteenth century, as a city of little importance and alternately part of the provinces of Fars, Kerman and Khurasan. The invasion and unstable rule by the Ghalzai Afghans in the 1720s furthered the city's deterioration with little new development till 1747. A succession of able governors beginning with Mohammad Taqi Khan (1747-1798) partially restored the city's lost glory with construction and repair of qanats, villages, gardens, caravan-serais and defense outposts. 

Yazd's existence in an arid region was made possible by an extensive system of sloping subterranean man made infiltration tunnels which conduit fresh water from the surrounding highlands. Some of these conduits, called qanats are as long as 50 kilometres in length, though the most do not exceed five kilometres. The extreme climate also evolved architecture obsessed with insulation by mud bricks and thick walls as well as cooling by ventilation structures called badgirs. A badgir is a vertical wind catching structure on the roof that directs and cools trapped wind over small water pools within the building. 

Sources: 

Bonine, Michael Edward. "Yazd and its Hinterland: A central place system of dominance in the central Iranian plateau." Unpublished doctoral dissertation, University of Texas at Austin, 1975.

Lockhardt, Laurence. Persian Cities. London: Luzac & Company, 1960.

"Yazd City,  Yazd Province." Iran Travel and Tourism Organization. http://www.yazdcity.com/english/indexen.htm [Site inaccessible as of 11 August, 2016]

"Iranian Architecture." http://www.irania.tv/city/yazd/ [Site inaccessible as of 11 August, 2016]