The theoretical modelling of structure-property relationships from the nano- to the meso-scale requires the synergistic use of various simulation methodologies. Electronic and magnetic properties of, e.g., molecules, nano-wires or oxide layers are studied by quantum mechanical methods, via the development and application of electronic density functional techniques. Molecular arrangements and properties on longer length scales of, e.g., macromolecules or magnetic model systems, are studied by Molecular Dynamics and Monte Carlo techniques. Heterogeneous structures on still larger scales are mapped onto field-theoretical descriptions and treated with tools of numerical mathematics. Different techniques are used to bridge multiple time- and length-scales to characterise and understand the functions of complex structures. The use of such computational methods to explore and predict the properties of novel, engineered materials is an emerging discipline of considerable current interest.