In this talk, I will introduce the motivation and basic ideas of model order reduction, briefly review its development from projection-based methods to modern data-driven approaches, and discuss several fundamental challenges, including nonlinear complexity, stability, accuracy beyond the training regime, and the preservation of physical structure. I will then focus on operator inference, a nonintrusive framework that learns reduced operators directly from simulation data. For Hamiltonian and port-Hamiltonian systems, unconstrained learning may destroy conservation laws, dissipation properties, or passivity, leading to unreliable long-time predictions. I will describe structure-preserving operator inference methods that incorporate the underlying geometric and physical structure into the learning process. Numerical examples will illustrate how combining data with mathematical structure can produce reduced models that are both efficient and physically meaningful.