All buildings must stand. An adequate structure was as necessary for the simplest primitive hut as it is for the tallest or widest-spanning modern building. However, this requirement became more difficult to satisfy as designers became more adventurous and the experience already gained became less directly applicable. The present papers look at the consequent evolution of design methods and the types of understanding that have been essential guides. A particular focus is the question of how earlier innovations, made without the benefits of modern theory, were possible. Other papers look in detail at the most outstanding of these achievements, such as the church of Hagia Sophia in Istanbul and the dome of Florence Cathedral.