This article surveys recent progress in the Bradley-Terry (BT) model and its extensions. We focus on the statistical and computational aspects, with emphasis on the regime in which both the number of objects and the volume of comparisons tend to infinity, a setting relevant to large-scale applications. The main topics include asymptotic theory for statistical estimation and inference, along with the associated algorithms. We also discuss applications of these models, including recent work on preference alignment in machine learning. Finally, we discuss several key challenges and outline directions for future research.

翻译：本文综述了布拉德利-特里模型及其扩展形式的最新研究进展。我们重点关注该模型的统计与计算特性，尤其着眼于对象数量与比较数据量均趋于无穷的渐近情形——这一设定与大规模实际应用密切相关。核心内容涵盖统计估计与推断的渐近理论，以及相关的计算算法。同时，我们探讨了这些模型在机器学习偏好对齐等前沿领域的应用实例。最后，本文讨论了该领域面临的若干关键挑战，并对未来研究方向进行了展望。