Physics-informed neural networks (PINNs) have proven to be a transformative approach to modeling the behavior of physical systems. They have proven highly effective by leveraging available measurements and a parameterized PDE in a semi-supervised learning framework. However, PINNs are limited to specific boundaries, initial conditions, and loading or source terms and require extensive training during inference. This restricts their effectiveness for various operating conditions and real-time inference, although transfer learning can somewhat mitigate this issue. What the field of engineering needs is a more adaptable version of PINNs that can rapidly infer the system’s response for a wide range of boundary/initial conditions, loadings, and domain geometry without necessitating extensive retraining. Such advancements, i.e. neural operator, could enable computation speeds thousands of times faster than those achievable through traditional numerical methods. In this chapter, we introduce the two most important methods in neural operators, namely, DeepONet and the Fourier Neural Operator (FNO). We then present several examples demonstrating the combination of DeepONet and FNO in engineering applications.