Carbon nanotubes (CNT) and graphene have been one of the noticeable research areas in science and technology. In recent years, the assembly of these carbon nanostructures is one of the most interesting topic to the scientific world due to its variety of applications from nano to macroscale. These bulk nanostructures to be applicable in shock absorbers, batteries, sensors, photodetectors, actuators, solar cells, fuel cells etc. The present work is motivated to study the detailed compressive behavior of three dimensional cellular assemblies of CNT and graphene. The CNT foams are synthesized by chemical vapor deposition method. It is interesting to study the compressive behavior of CNT foam in the presence external magnetic field applied perpendicular to CNT axis. The peak stress and energy absorption capability of CNT foam enhances by four and nearly two times in the presence of magnetic field as compared to the absence of the magnetic field. In the absence of magnetic field the deformation of CNT foam is obtained elastic, plateau and densification regions. Further CNT foam is loaded with iron oxide nanoparticles of diameter is ~ 40nm on the surface and detailed study of the compressive behavior of the foam by varying iron nanoparticles concentration. The peak stress and energy absorption capability of CNT foam initially decreases with increasing the intensity of the magnetic field, further increases the intensity of the magnetic field the maximum stress and energy absorption capability increases which is due to magnetic CNT and particles align in the direction of the magnetic field. CNT surfaces were further modified by fluid of different viscosities. The mechanical behavior of CNT foam filled with fluids of varying viscosities like 100%, 95% and 90% glycerol and silicone oil are 612, 237, 109 and 279 mPa-s respectively. The mechanical behavior of CNT foam depends on both the intensity of magnetic field and fluid viscosity. The non linear relation between peak stress of CNT and magnetic field intensity is σp(B, η) = σ0 ± α(B-B0) where σ0 is the peak stress at B = B0 , η is the fluid viscosity, parameter α depends on properties of the MR fluid and B0 is an optimum magnetic field for which peak stress is maximum or minimum depending on the fluid viscosity. Graphene is assembled into a three dimensional structure called graphene foam. The graphene foam is infiltrated with polymer and study the detailed compressive behavior of graphene foam and graphene foam/PDMS at different strains of 20, 40, 60 and 70%. The maximum stress and energy absorption capability of graphene foam/PDMS is six times higher than the graphene foam. Also the graphene foam/PDMS is highly stable and reversible for 100 cycles at strains of 30 and 50%. The mechanical behavior of CNT, graphene foam, CNT/PDMS and graphene foam/PDMS is compared. Among all the foams, graphene foam/PDMS has shown the highest elastic modulus as compared to other foams. This behavior can be attributed to the wrinkles formation during the growth of graphene and a coupling between PDMS and interfacial interactions of graphene foam. Therefore it suggests potential applications for dampers, cushions and electronic packaging. Furthermore, the interaction between nanoparticles and polymer in a novel architecture composed of PDMS and iron oxide nanoparticles is studied. The load bearing capacity of uniform composites enhanced by addition of nanoparticles, reaching to a maximum to 1.5 times of the PDMS upon addition of 5wt.% of nanoparticles, and then gradually decreased to 1/6th of PDMS upon addition of 20wt.% of nanoparticles. On the other hand, the load bearing capacity of architectured composites at high strains (≥40%) monotonically increased with addition of nanoparticles in the pillars.