We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales.

我们回顾了在宇宙学尺度上测试广义相对论（GR）的最新进展和结果。在过去的二十年中，这一主题经历了快速发展，旨在解决宇宙加速及其相关的暗能量问题。然而，随着精密宇宙学的出现，它本身也成为了在宇宙尺度上测试引力物理的一项积极的努力。我们概述了引力的宇宙学探测器、用于测试宇宙学尺度上的广义相对论偏差的形式主义和参数化、选定的修正引力（MG）理论、引力筛选机制以及为这些测试开发的计算机代码。然后，我们总结了最近对 MG 参数和选定的 MG 模型的宇宙学约束。我们通过最近双中子星合并事件的影响总结来补充这些宇宙学限制。接下来，我们总结了使用和不使用天体物理系统学的 MG 参数预测的一些结果，这些结果将主导不确定性。该评论旨在提供该主题的整体概况，并为有兴趣加入该领域的学生和研究人员提供切入点。它还可以作为对宇宙尺度上测试引力的最新结果和限制的快速参考。