Our research employs computer simulations and the tools of statistical mechanics to understand and predict the structural and mechanical behaviour of complex materials in and out of equilibrium. In addition to testing theories and discovering unexpected behavior, computer simulations reveal quantities that are difficult or impossible to obtain in experiments and thus greatly help reduce the effort to engineer new functional materials. We seek to explain molecular mechanisms that give rise to macroscopic material properties. Modeling phenomena on length and time scales that span from the atomistic to the continuum is achieved by a combination of density functional theory on the quantum level, classical molecular dynamics and Monte Carlo simulations on the atomic level and field theoretic (phase field) methods on the mesoscale. We study a diverse group of materials that include amorphous (nanostructured) polymers, metallic alloys, and biopolymers.