The field of operator learning and inverse problems is rapidly advancing with the development of novel methods and techniques. Recent research has focused on improving the accuracy and efficiency of operator learning methods, particularly in the context of nonlinear inverse problems. One notable direction is the use of neural operator learning methods, which have shown promise in approximating infinite-dimensional operators. Another area of research is the development of noise-aware operator learning frameworks, which can effectively handle noisy data and improve the robustness of inverse problem solutions. Furthermore, the use of convolutional neural networks and other deep learning architectures has been explored for solving inverse problems in various fields, including electromagnetic scattering and physics inversion. Overall, the field is moving towards the development of more accurate, efficient, and robust methods for solving inverse problems, with potential applications in a wide range of fields. Noteworthy papers include: Operator Learning at Machine Precision, which introduces a new operator learning paradigm that can achieve machine precision, and Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion, which proposes a lightweight bidirectional module that learns a local inverse of a differentiable forward surrogate. Extension and neural operator approximation of the electrical impedance tomography inverse map is also notable for its development of a noise-aware operator learning framework for electrical impedance tomography.