We present a current, up-to-date review of the surface hopping methodology for solving nonadiabatic problems, 25 years after Tully published the fewest switches surface hopping algorithm. After reviewing the original motivation for and failures of the algorithm, we give a detailed examination of modern advances, focusing on both theoretical and practical issues. We highlight how one can partially derive surface hopping from the Schrödinger equation in the adiabatic basis, how one can change basis within the surface hopping algorithm, and how one should understand and apply the notions of decoherence and wavepacket bifurcation. The question of time reversibility and detailed balance is also examined at length. Recent applications to photoexcited conjugated polymers are discussed briefly.

中文翻译：

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了解电子跃迁和退相干的表面跳变视图。

在Tully发布最少的开关表面跳变算法25年之后，我们介绍了用于解决非绝热问题的表面跳变方法的最新动态。在回顾了算法的最初动机和失败之后，我们对理论上和实践上的问题进行了详细的现代研究。我们重点介绍了如何在绝热基础上从Schrödinger方程中部分导出表面跳变，如何在表面跳变算法内改变基础，以及如何理解和应用去相干和波包分叉的概念。时间可逆性和详细平衡的问题也得到了详尽的研究。简要讨论了光激发共轭聚合物的最新应用。