In recent years, rapid advances in computational science, data-driven techniques, and machine learning have profoundly reshaped the landscape of model order reduction (MOR), model discovery, and surrogate modeling. This invited session brings together cutting-edge research at the intersection of physics-based modeling and data-driven methodologies, highlighting innovative strategies for constructing efficient, reliable, and interpretable reduced-order and surrogate models. Topics include projection-based MOR for nonlinear and time-dependent problems, data-driven and data assimilation methods leveraging sparse sensing and neural networks, and novel approaches to system identification and model discovery from limited or noisy data. Applications span a wide range of domains, including fluid dynamics, structural mechanics, multi-body dynamics and multi-physics systems. Emphasis is placed on the integration of physical laws, the handling of high-dimensional parameter spaces, and the development of robust methods for uncertainty quantification. The session aims to foster dialogue between theoretical development and practical implementation, and bridging traditional modeling approaches with modern data-centric techniques, paving the way for next-generation simulation tools.