Neural circuits have evolved to accommodate similar information processing challenges as those faced by engineered systems. Here, we compare neural versus engineering strategies for constructing networks. During circuit development, synapses are overproduced and then pruned back over time, whereas in engineered networks, connections are initially sparse and are then added over time. We provide a computational perspective on these two different approaches, including discussion of how and why they are used, insights that one can provide the other, and areas for future joint investigation. By thinking algorithmically about the goals, constraints, and optimization principles used by neural circuits, we can develop brain-derived strategies for enhancing network design, while also stimulating experimental hypotheses about circuit development and function.