Numerous methods have recently emerged for fabricating cellular lattice structures with unit cells that can be repeated to create 3D space filling systems with very high interconnected pore fractions. These lattice structures possess exceptional mechanical strength resulting in highly efficient load supporting systems when configured as the cores of sandwich panels. These same structures also provide interesting possibilities for cross flow heat exchange. In this scenario, heat is transported from a locally heated facesheet through the lattice structure by conduction and is dissipated by a cross flow that propagates through the low flow resistant pore passages. The combination of efficient thermal conduction along the lattice trusses and low flow resistance through the pore channels results in highly efficient cross flow heat exchange. Recent research is investigating the use of hollow truss structures that enable their simultaneous use as heat pipes which significantly increases the efficiency of heat transport through the lattice and their mechanical strength. The relationships between heat transfer, frictional flow losses and topology of the lattice structure are discussed and opportunities for future developments identified.