The interaction of nano particles with conventional materials dramatically changes all the physical parameters, which usually characterize the bulk material. The nano particles constitute highly reactive isolated sites to the extent that it leads to a change in the electronic structure of the nano composite, and accordingly all the physical properties, such as thermal, mechanical and electrical properties become different from those of the bulk material. To successfully exploit nano composites as components and devices, this fundamental shift of physical properties must be properly understood and accurately modelled. While experimentation is crucial, a theoretical understanding is also necessary and with changed physical parameters, existing continuum theories may still be able to capture critical phenomena. This paper provides an introduction to some of the issues and the theoretical developments in nanotechnology involving the three topics of the enhanced thermal conductivity of nanofluids, electrorheological fulids and the mechanics of carbon nanotubes. It is presented with a view to identifying those areas where applied mathematical modelling might yield important insights.