Graphene is a two-dimensional material that offers a unique combination of exceptional mechanical properties, large surface area, and excellent electrical conductivity. The extension into three-dimensional graphene (3DG) foam assemblies, however, has been hampered by significant degradation of these properties particularly when scaling to lower densities. While existing 3D printing methods (e.g., extrusion, ice-templating, laser templating, casting) have produced 3DGs, these techniques only allow limited structural control and printed features are macroscale in size; no current technique has been able to create graphene with arbitrary, highly connected three-dimensional form factors and microscale features to truly bring the benefits of 3D micro-architectures to 3DGs.  Existing methods have all fallen short in achieving a truly arbitrary design space due to limitations in both the printing technique (e.g. toolpath requirement, serial writing) and feedstock materials which are typically not self-supporting.  Present 3DGs are still constrained to only a few bending-dominated design geometries (woodpile, square array etc.) and relatively large ligament feature sizes (>100 μm), which preclude the vast design freedom to create 3D graphene mesoscale architectures for applications in energy storage and conversion.