Social insect nest architectures can be complex, intricate structures. Stigmergy (see section 1.2.3), that is, the coordination of activities through the environment, is an important mechanism underlying nest construction in social insects. Two types of stigmergy are distinguished: quantitative, or continuous stigmergy, in which the different stimuli that trigger behavior are quantitatively different; and qualitative, or discrete stigmergy, in which stimuli can be classified into different classes that differ qualitatively. If quantitative stigmergy can explain the emergence of pillars in termites, the building behavior of the paper wasps Polistes dominulus seems to be better described by qualitative stigmergy. In this chapter, a simple agent-based model inspired by discrete stigmergy is introduced. In the model, agents move in a three-dimensional grid and drop elementary building blocks depending on the configuration of blocks in their neighborhood. From the viewpoint of bricks, this model is a model of self-assembly. The model generates a large proportion of random or space-filling forms, but some patterns appear to be structured. Some of the patterns even look like wasp nests. The properties of the structured shapes obtained with the model, and of the algorithms that generate them, are reviewed. Based on these properties, a fitness function is constructed so that structured architectures have a large fitness and unstructured patterns a small fitness. A genetic algorithm based on the fitness function is used to explore the space of architectures. Several examples of self-assembling systems in robotics, engineering, and architecture are described. Self-assembling or self-reconfigurable robotic systems, although they are not directly inspired by nest construction in social insects, could benefit from the discrete-stigmergy model of nest building. The method of evolutionary design, that is, the creation of new designs by computers using evolutionary algorithms, is a promising way of exploring the patterns that self-assembling models can produce. Many animals can produce very complex architectures that fulfill numerous functional and adaptive requirements (protection from predators, substrate of social life and reproductive activities, thermal regulation, etc.).