Branched hierarchical micro-truss structures may be incorporated into energy-absorbing structures to exhibit a tailored multi-stage buckling response to a range of different compressive loads. Branched hierarchical micro-truss structures may also be configured to function as vascular systems to deliver fluid for thermal load management or altering the aerodynamic properties of a vehicle or structure into which the branched hierarchical micro-truss structure is incorporated. The branched hierarchical micro-truss structure includes a first layer having a series of interconnected struts and a second layer having a series of struts branching outward from an end of each of the struts in the first layer.