Heuristic computation techniques have been used in a wide range of fields, demonstrating their capacity to solve highly complex optimization problems. This article presents the most common techniques and their extension into the multi-objective optimization field, and emphasizes in the application of them in structural and architectural design by presenting examples within topics like: topological, shape and dimensional optimization of truss structures, roof optimization for sunlight conditions and area minimization, grid structures, façade design, life cycle cost and environmental impact, energy efficiency and construction costs, morphogenetic structural optimization for shell structures, acoustical optimization, evolutionary architectural design, architectural layout design optimization, RC frames optimization, and land use zoning, within others. Finally, the conclusion leads to the recognition of heuristic computation not only as an optimization tool, but also as an important component of a design methodology for creating innovative, creative, efficient, well performing, and aesthetically pleasant architectural/engineering objects.