During the past decades of the last century researchers concentrated on optimizing mesh-based methods for the solution of partial differential equations in applied mathematics and engineering, e.g. error controlled adaptive meshing, sophisticated constitutive modeling. Beginning of the recent century people recognized, that despite all progress in computer resources and in the algorithmic treatment of discretized systems, for example so called multi-query problems could never be treated with classical mesh-based methods. The success-story of model-order reduction (MOR) has been initiated. Examples for multi-query problems are for example optimization and inverse problems, parametric and uncertainty propagation as-well-as multi-scale problems in space and time. Nowadays a bunch of methods are available, like proper-orthogonal decomposition (POD), proper-generalized decomposition (PGD) or machine-learning (ML) techniques. In general, they can be distinguished in intrusive and non-intrusive methods, depending on the specific coding effort. Nonetheless, a challenge remains on the efficient treatment of non-linear and high-dimensional problems. Thus, the focus of this mini-symposium will be on latest developments and sophisticated application of MOR for non-linear and high-dimensional problems in solid and fluid mechanics, including methods augmented with experimental data (data augmented simulations (DAS)).