Advanced CSS Grid Techniques for Responsive Web Design

How can developers use advanced CSS Grid techniques to create highly responsive and dynamic layouts for modern web design? Discuss the use of grid-template-areas for better semantic structure, as well as the implementation of auto-fill and auto-fit properties to create fluid designs. How can CSS Grid be combined with Flexbox to achieve complex, nested layouts that remain flexible across different screen sizes? What are the potential challenges of relying heavily on CSS Grid, especially when considering browser compatibility and performance?