Since its inception, Mean Field Game (MFG) theory has developed rapidly and is increasingly applied across diverse domains such as economics, finance, energy systems, biology, and sociology. This paper explores new research directions in MFGs, focusing on practical applications. We discuss theoretical and computational challenges in analyzing monotone and non-monotone MFGs (where agent costs do not necessarily increase with population density), highlighting their relevance in modeling phenomena such as traffic flow. We also explore the role of boundary conditions in MFG models, illustrating how they influence solutions and the interpretation of results, especially in models dealing with agent flow at the boundaries. Our work highlights the importance of empirical calibration of MFG models, utilizing real-world data to refine model accuracy and parameter estimation. Moreover, we examine the integration of machine learning methods into MFG research, demonstrating their potential to enhance computational efficiency and provide innovative solutions to high-dimensional problems typical of mean-field models.