Nanotechnology is currently an area of intense research activity. To date there is some limited experimental data, and considerably more computational data arising from molecular dynamics simulations, but there is very little applied mathematical modelling from the disciplines associated with modelling, namely mathematics and mechanics. This paper reviews some of the mathematical and mechanical modelling contributions for interacting molecular structures. Modelling can indicate to the experimentalist materials and geometry where a certain outcome may be anticipated. A combined modelling—computational approach can make efficient a computational procedure that alone is not practical. The present review aims to provide an overview of contributions to date, but is necessarily focussed on the work of the present authors, since the number of mathematically orientated workers in the field is limited.