In this paper, we first give an introduction to the theoretical basis of the privacy-utility equilibrium in federated learning based on Bayesian privacy definitions and total variation distance privacy definitions. We then present the \textit{Learn-to-Distort-Data} framework, which provides a principled approach to navigate the privacy-utility equilibrium by explicitly modeling the distortion introduced by the privacy-preserving mechanism as a learnable variable and optimizing it jointly with the model parameters. We demonstrate the applicability of our framework to a variety of privacy-preserving mechanisms on the basis of data distortion and highlight its connections to related areas such as adversarial training, input robustness, and unlearnable examples. These connections enable leveraging techniques from these areas to design effective algorithms for privacy-utility equilibrium in federated learning under the \textit{Learn-to-Distort-Data} framework.