Operator learning has undergone rapid development in recent years and gradually emerged as a transformative machine-learning paradigm. In this talk, I will provide an overview of the operator-learning framework and explore its applications to computational problems, with a particular focus on quantum many-body dynamics. We will discuss how traditional machine learning models, such as recurrent neural networks (RNNs), can be adapted to learn operators and predict the nonequilibrium dynamics of quantum many-body systems. Additionally, I will highlight how transformer-based neural operators can be employed to model the self-energy of strongly correlated systems. Through these examples, we aim to showcase the potential of operator learning to tackle key challenges in quantum many-body systems, especially when the dynamics are high-dimensional but not necessarily chaotic.