Predicting real-time complex dynamics in physical systems governed by partial differential equations (PDEs) is challenging due to the computational expense of conventional numerical simulations. Neural operators offer a promising solution by approximating mappings between infinite-dimensional Banach spaces. However, their performance diminishes with increasing system size and complexity when trained on labeled observational data from high-fidelity simulators. In this presentation, I introduce a novel method for learning neural operators in latent spaces, enabling real-time predictions for systems with highly nonlinear and multiscale dynamics on high-dimensional domains. Leveraging the DeepONet architecture, the approach operates on a low-dimensional latent space encoding the dynamics of interest to efficiently and accurately approximate underlying operators. The efficacy of this approach is demonstrated across various real-world problems such as material fracture, stiff chemical kinetics, and global-scale climate modeling. Our method surpasses state-of-the-art techniques in prediction accuracy while significantly enhancing computational efficiency, thus enabling operator learning on previously infeasible scales.