Medieval cities varied substantially in their water supply as growing urban areas in Britain, continental Europe and the Islamic world all had different solutions. Although this reply won't go into details, some of the biggest engineering innovations at this time were actually in how to route and dispose of waste water, rather than drinking water.

In most of medieval Britain, wells were the main form of water supply. Wells had previously been used in the ancient world, for example in Roman country estates, but their use and development accelerated greatly in the medieval period. The 4th Century saw the use of terracotta drums and similar lining methods to protect wells and provide ease of water access. In the Early Middle Ages, when larger towns formed primarily around castles, wells were commonly placed in the innermost keeps, sometimes in basements or built with the well head reaching the first storey. Depending on the area, these could be prone to drying up but were, for the most part, a reliable source of water. In the 15th-17th Centuries, the digging of artificial canals, particularly to supply larger cities like London, became more common. The New River is the most famous example of this, but other artificial waterways preceded it, typically conveying water from rivers and meetings fresh input sources like wells and springs along their course. These artificial waterways were commonly leats, basically an in-ground aqueduct that often supplied ponds or watermills (Merdinger, 1955).

In continental Europe, larger cities were often reliant on older, still extant Roman aqueducts. However, they required constant upkeep which kept their use limited in both scope and time. For approximately five centuries after the fall of the empire, Roman aqueducts were still being used and somewhat maintained throughout some Spanish, Italian and French regions. However, the use of cisterns, wells and leats soon became more dominant as these were less reliant on centralised power and authority providing funding for maintenance. Notably, while most large cities were built near rivers, drinking running river water was rare. Rivers were used more frequently for channelling waste water, washing and leisure. This is not to say that the knowledge of aqueducts was lost. Although there are some historical sources indicating confusion about aqueducts (such as a 1436 account that suggested they were dangerous and used for watering horses), similar technology was used to supply waterwheels and in the bread-making industry. The Spanish also demonstrated some improvements with more efficient use of resources to repair aqueducts with fewer arches, longer spans, etc. (Deming, 2019)

In the medieval Islamic world, ambitious civil engineering projects saw water sourced from wells, aqueducts and later through indoor plumbing systems relying on pumps. Hydraulic systems provided fresh water through a network of pipes (ranging from wooden to clay) that were capable of providing water to even multiple-storey tenement buildings (Chant and Goodman, 2020).

So, aqueducts did not disappear entirely, though most certainly did fall into disrepair. They required a bureaucracy and engineering corps that most medieval societies simply lacked. In Britain especially, most engineering knowledge related to water supply was kept by the clergy, with monasteries often having impressive sewer and water supply works. Eventually this knowledge was passed onto lay labourers in larger cities (Merdinger, 1955). The result was greater use of simplified, lower maintenance wells, cisterns and canals. Eventually this gave way to indoor plumbing supplied by pumped water. However, there were significant differences across the medieval world.