Insects build myriad structures out of diverse materials. These structures serve purposes that range from facilitating prey capture to housing their entire colony. Whereas some insects operate solitarily, others collectively build large and complex structures. The architecture of these structures vis-à-vis their ultimate function poses fascinating questions that require multidisciplinary investigations. Importantly, because the underlying design and architectural principles have evolved over millions of years to withstand multitude of environmental perturbations, they offer important lessons for human-made structures. The vast variety of insect-built structures reflects how diverse insects have adapted to resolve the ecological challenges in their specific habitats. Here, we survey insect-built structures from a comparative perspective to ask what design and architectural principles can be gleaned from them. We discuss the key hypotheses about building-behaviours, their neural underpinnings, the functional role of insect-built structures and their biomimetic potential.