The study of 4-dimensional N=2 supersymmetric field theories has been a focal point since Seiberg and Witten's groundbreaking work. Particularly, when these theories exhibit conformal behavior, an intriguing link emerges between their low-energy dynamics and the Hitchin system—a rich mathematical structure. This integrable system offers a geometric framework for comprehending these theories. By extending this framework globally, one can construct a family of Hitchin systems, enabling the study of superconformal field theories within a broader family context. The interplay between mathematics and physics enables answering important questions on both sides, leveraging the machinery from one field to advance understanding in the other.