Thermal conductivity(k) is an important property of a material which is critical for applications in thermal management applications as well as thermoelectric energy conversion devices. In this work, we study the thermal transport in various materials such as polymers, polymer nanocomposites and semiconductors with different applications. Thermal conductivity (k) of polymers is significantly lower than metals. As an example, k of bulk polyethylene is ~ 0.5 W/m-K while k of aluminum is 200 W/m-K. This limits their applications in thermal management systems. Polymers, however, offer many potential advantages such as low cost, low weight, corrosion resistance and ease of processability which makes them attractive for heat transfer applications. Enhancement in thermal conductivity of polymers would enable materials to replace metals in heat transfer applications, allowing these unique advantages to be realized in commercial thermal management technologies. Similarly, accurate understanding of thermal conduction in semiconductor materials is of vital importance for designing thermal management solutions for electronics systems. The goals of this work are to enhance k of polymers through– a) alignment of polymer lamellae and embedded graphene nanoplatelets. It has been reported that, an almost 30-fold increase in thermal conductivity of aligned polyethylene was achieved demonstrating the large potential of alignment effects. Our group also achieved a 12-fold increase in thermal conductivity of simultaneously aligned polymer lamellae and graphene nanoplatelets (GnPs), and b) enhancement of interface thermal conductance between polymer and graphene through the novel effect of edge-bonding. Recently edge-bonding was shown to nearly 2-fold enable superior interface thermal conductance relative to basal-plane bonding. These effects will be studied using molecular dynamics (MD) simulations. C) thermal conductivity modulation (both increase and decrease) of semiconductors through biaxial strain for applications in thermal management and thermoelectric energy conversion d) semiconductor materials with ultra-high thermal conductivity e) 2D semiconductors. We employed density functional perturbation theory (DFPT) coupled with exact solution of phonon Boltzmann transport equation (PBTE) for predicting the k of semiconductors.