This paper surveys recent studies on mean-field models, inspired by Statistical Mechanics and Physics. The authors present three examples of their mean-field approach in Economics and Finance. The models involve a large number of rational players with limited information, who make optimal decisions based on global information resulting from all players' actions. The mean-field problems derived are nonlinear differential equations of a new type, studied here to understand their mathematical properties and connections to various fields of Analysis. The authors show that these problems are essentially well-posed, having unique solutions. They also discuss various limiting cases, examples, and possible extensions, as well as mention many open problems. The paper is structured as follows: an introduction, sections on mean-field games, price formation and dynamic equilibria, and the formation of volatility, each with subsections detailing the models, results, and analyses. The introduction provides a general overview of the economic and financial contexts addressed through the mean-field approach. The authors emphasize the derivation of these models from a "continuum limit," similar to classical mean field approaches in Statistical Mechanics and Physics. They also highlight the connection to various research areas in Analysis and the importance of studying these new nonlinear equations. The paper concludes with a brief overview of the economic and financial issues addressed through the mean-field approach.This paper surveys recent studies on mean-field models, inspired by Statistical Mechanics and Physics. The authors present three examples of their mean-field approach in Economics and Finance. The models involve a large number of rational players with limited information, who make optimal decisions based on global information resulting from all players' actions. The mean-field problems derived are nonlinear differential equations of a new type, studied here to understand their mathematical properties and connections to various fields of Analysis. The authors show that these problems are essentially well-posed, having unique solutions. They also discuss various limiting cases, examples, and possible extensions, as well as mention many open problems. The paper is structured as follows: an introduction, sections on mean-field games, price formation and dynamic equilibria, and the formation of volatility, each with subsections detailing the models, results, and analyses. The introduction provides a general overview of the economic and financial contexts addressed through the mean-field approach. The authors emphasize the derivation of these models from a "continuum limit," similar to classical mean field approaches in Statistical Mechanics and Physics. They also highlight the connection to various research areas in Analysis and the importance of studying these new nonlinear equations. The paper concludes with a brief overview of the economic and financial issues addressed through the mean-field approach.