Carbon nanotubes and graphene are almost perfect molecules with truly amazing combinations of thermal, electrical, and structural properties. However, to harvest their full potential they need to be fully integrated as hybrid materials in all sorts of matrices. Full integration requires their development beyond conventional composites so that the level of the non-nano material is designed to integrate fully with the molecules of carbon nanotubes and graphene. Here the nano materials are part of the matrix rather than a differing component, as in the case of conventional composites. To advance the development of multifunctional materials integrating nanotubes and graphene, this research is focused on the simultaneous control of the nano architecture, structural properties, the thermal and the electrical conductivity of fully integrated nano hybrid materials systems. These hybrid materials systems are designed to surpass the limits of rule of mixtures in conventional composite design. The goals are to implement multifunctional designs to fully mimic the properties of carbon nanotubes and graphene on larger scales, from the nano, to the meso, to the micro and to the macro scales, and to enhance the thermal and electrical the management, in addition to the control of other properties such as mechanical strength and fracture toughness. These new approaches involve exfoliation, functionalization, dispersion, stabilization, alignment, polymerization, reaction bonding and coating, designed to achieve full integration. Typical examples of structural applications of polymeric and ceramic matrices and applications in energy systems such as capacitors and batteries as well as other material systems are presented and discussed.