Polymer nanocomposite foams have attracted tremendous interests due to their multifunctional properties in addition to the inherited lightweight benefit of being foamed materials. Polymer nanocomposite foams using high performance polymer and bio-degradable polymer with carbon nanotubes were fabricated, and the effects of foam density and pore size on properties were characterized. Electrical conductivity modeling of polymer nanocomposite foams was conducted to investigate the effects of density and pore size. High performance polymer Polyetherimide (PEI) and multi-walled carbon nanotube (MWCNT) nanocomposites and their foams were fabricated using solvent-casting and solid-state foaming under different foaming conditions. Addition of MWCNTs has little effect on the storage modulus of the nanocomposites. High glass transition temperature of PEI matrix was maintained in the PEI/MWCNT nanocomposites and foams. Volume electrical conductivities of the nanocomposite foams beyond the percolation threshold were within the range of electro-dissipative materials according to the ANSI/ESD standard, which indicates that these lightweight materials could be suitable for electro-static dissipation applications with high temperature requirements. Biodegradable Polylactic acid (PLA) and MWCNT nanocomposites and their foams were fabricated using melt-blending and solid-state foaming under different foaming conditions. Addition of MWCNTs increased the storage modulus of PLA/MWCNT composites. By foaming, the glass transition temperature increased. Volume electrical conductivities of foams with MWCNT contents beyond the percolation threshold were again within the range of electro-dissipative materials according to the ANSI/ESD standard. The foams with a saturation pressure of 2 MPa and foaming temperature of 100 °C showed a weight reduction of 90% without the sacrifice of electrical conductivity. This result is promising in terms of multi-functionality and material saving. At a given CNT loading expressed as volume percent, the electrical conductivity increased significantly as porosity increased. A Monte-Carlo simulation model was developed to understand and predict the electrical conductivity of polymer/MWCNT nanocomposite foams. Two different foam morphologies were considered, designated as Case 1: volume expansion without nanotube rearrangement, and Case 2: nanotube aggregation in cell walls. Simulation results from unfoamed nanocomposites and the Case 1 model were validated with experimental data. The results were in good agreement with those from PEI/MWCNT nanocomposites and their foams, which had a similar microstructure as modeled in Case 1. Porosity effects on electrical conductivity were investigated for both Case 1 and Case 2 models. There was no porosity effect on electrical conductivity at a given volume percent CNT loading for Case 1. However, for Case 2 the electrical conductivity increased as porosity increased. Pore size effect was investigated using the Case 2 model. As pore size increased, the electrical conductivity also increased. Electrical conductivity prediction of foamed polymer nanocomposites using FEM was performed. The results obtained from FEM were compared with those from the Monte-Carlo simulation method. Feasibility of using FEM to predict the electrical conductivity of foamed polymer nanocomposites was discussed. FEM was able to predict the electrical conductivity of polymer nanocomposite foams represented by the Case 2 model with various porosities. However, it could not capture the pore size effect in the electrical conductivity prediction. The FEM simulation can be utilized to predict the electrical conductivity of Case 2 foams when the percolation threshold is determined by Monte-Carlo simulation to save the computational time. This has only been verified when the pore size is small in the range of a few micrometers. / text