This contribution presents a unified perspective on leveraging Optimal Transport (OT) theory to address computationally intensive challenges in scientific computing, encompassing efficient OT solvers and advanced OT-inspired Reduced Order Models (ROMs). We first detail numerical strategies to accelerate regularized semi-discrete optimal transport (RSOT) solvers [1]. By combining distance-based truncation, R-tree spatial queries, multilevel hierarchies, and regularization scheduling, we significantly reduce computational costs for large- scale RSOT problems. Second, OT-based displacement interpolation is leveraged for data augmentation in ROMs for advection-dominated systems [2]. This enriches sparse datasets with synthetic snapshots. Com- bined with time-parameter mapping and POD-Gaussian Process Regression correction, it im- proves predictive accuracy and enables continuous-time solutions for complex flows. Furthermore, a deep learning ROM framework addresses slow-decaying Kolmogorov n-width problems [3]. This integrates Kernel Proper Orthogonal Decomposition (kPOD) with a Wasserstein- derived kernel and autoencoders, trained using Sinkhorn divergence as a loss function. The approach effectively captures geometric data structures, outperforming traditional ROMs. Collectively, these methodologies showcase OT’s versatility in reducing computational costs and improving model fidelity for complex scientific applications, advancing both direct OT computation and OT-enhanced surrogate modeling. [1] Khamlich, M., Romor, F., and Rozza, G. Efficient numerical strategies for regularized semi- discrete optimal transport. (In preparation) [2] Khamlich, M., Pichi, F., Girfoglio, M., Quaini, A., and Rozza, G. Optimal transport-based displacement interpolation with data augmentation for reduced order modeling of nonlinear dynamical systems. Journal of Computational Physics. [3] Khamlich, M., Pichi, F., and Rozza, G. Optimal Transport–Inspired Deep Learning Frame- work for Slow-Decaying Kolmogorov n-Width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel. SIAM Journal on Scientific Computing.