Tracking and identifying athletes on the pitch holds a central role in collecting essential insights from the game, such as estimating the total distance covered by players or understanding team tactics. This tracking and identification process is crucial for reconstructing the game state, defined by the athletes' positions and identities on a 2D top-view of the pitch, (i.e. a minimap). However, reconstructing the game state from videos captured by a single camera is challenging. It requires understanding the position of the athletes and the viewpoint of the camera to localize and identify players within the field. In this work, we formalize the task of Game State Reconstruction and introduce SoccerNet-GSR, a novel Game State Reconstruction dataset focusing on football videos. SoccerNet-GSR is composed of 200 video sequences of 30 seconds, annotated with 9.37 million line points for pitch localization and camera calibration, as well as over 2.36 million athlete positions on the pitch with their respective role, team, and jersey number. Furthermore, we introduce GS-HOTA, a novel metric to evaluate game state reconstruction methods. Finally, we propose and release an end-to-end baseline for game state reconstruction, bootstrapping the research on this task. Our experiments show that GSR is a challenging novel task, which opens the field for future research. Our dataset and codebase are publicly available at https://github.com/SoccerNet/sn-gamestate.