In game theory, a game refers to a model of interaction among rational decision-makers or players, making choices with the goal of achieving their individual objectives. Understanding their behavior in games is often referred to as game reasoning. This survey provides a comprehensive overview of a fast-developing game-reasoning framework for large games, known as Policy Space Response Oracles (PSRO). We first motivate PSRO, provide historical context, and position PSRO within game-reasoning approaches. We then focus on the strategy exploration issue for PSRO, the challenge of assembling an effective strategy portfolio for modeling the underlying game with minimum computational cost. We also survey current research directions for enhancing the efficiency of PSRO, and explore the applications of PSRO across various domains. We conclude by discussing open questions and future research.