Models of realistic nonlinear structures are characterized by very high dimensionality that renders full-system simulations infeasible. Despite the broad availability of dedicated software packages, the prediction and continuation of steady-state response in such systems remains a serious computational challenge for full-scale nonlinear finite element models. The recent theory of Spectral Submanifolds (SSM) has laid the foundation for a rigorous model reduction of such nonlinear systems, leading to reliable steady-state response predictions within feasible computation times. Further developments have made the direct computation of such invariant manifolds and their reduced dynamics scalable to realistic, nonlinear finite-element models.

In this talk, we survey the basics of SSM theory and show how SSMs can be used to achieve an exact model reduction for realistic finite-element models of complex systems. We also mention recent technical developments, and survey applications to modelling and prediction in structural vibrations using direct as well as data-driven methods.