How did medieval builders manage to construct some of the tallest structures in the world without access to modern engineering theories? Construction drawings were limited to details and, with only a handful exceptions, manuals for builders only appeared in the late fifteenth century. By implication, the relevant knowledge had to be transferred on a personal basis. Its underlying principles must therefore have been reasonably simple. This article shows how a modular design, combined with on-site experimentation, guided much of the construction work on large projects such as European cathedrals, Middle Eastern mosques, Indian temples, and Chinese pagoda towers.