This lecture will present new computational form-finding and optimization approaches for exploring three-dimensional equilibrium shell structures, based on the stability analysis of the Gothic masonry vaults. Thanks to the intuitive graphical methods, the designer gains control over the exploration of form, which allows designing vaults with little or low-quality materials, or designing efficient and expressive surface structures. Several projects will demonstrate the power of these innovative methods for the safety assessment of historic masonry vaults with complex geometries and for the design and engineering of novel masonry shells, which range from sustainable construction solutions for developing countries to unique unreinforced vaults in tile or cut stone. The last part of the lecture will demonstrate how we can learn from the Master Builders to design better – well beyond masonry.