Architected materials that consist of periodic arrangements of nodes and struts are lightweight and can exhibit combinations of properties (such as negative Poisson ratios) that do not occur in conventional solids. Architected materials reported previously are usually constructed from identical `unit cells' arranged so that they all have the same orientation. As a result, when loaded beyond the yield point, localized bands of high stress emerge, causing catastrophic collapse of the mechanical strength of the material. This `post-yielding collapse' is analogous to the rapid decreases in stress associated with dislocation slip in metallic single crystals. Here we use the hardening mechanisms found in crystalline materials to develop architected materials that are robust and damage-tolerant, by mimicking the microscale structure of crystalline materials—such as grain boundaries, precipitates and phases. The crystal-inspired mesoscale structures in our architected materials are as important for their mechanical properties as are crystallographic microstructures in metallic alloys. Our approach combines the hardening principles of metallurgy and architected materials, enabling the design of materials with desired properties.