Many naturally occurring and engineered products are influenced by network structures. Collagen networks provide a scaffold for living tissue, while swollen arrays of physically cross-linked polypeptides constitute gelatin, the familiar dessert and electrophoresis medium. Although the associated mesh sizes differ by several orders of magnitude, these examples share a common feature: three-dimensional connectivity that imparts mechanical rigidity. Intercalating additional interconnected components can yield broader functions, e.g., ionic or electrical conductivity, optical band gaps, and tailored heat and mass transfer.