General relativity (GR) was proven via the direct detection of gravitational waves from the mergers of the binary black holes and binary neutron stars by the advanced LIGO and advanced virgo detectors. These detections confirmed the prediction of GR and provided the first direct evidence of the existence of stellar-mass black holes (BHs). However, the occurrence of singularities at the centers of BHs suggests that GR is inapplicable because of the breakdown of the equivalence principle at the singularities. The fact that these singularities exist indicates that GR cannot be a universal theory of space–time. In the low-energy limit, the theoretical and observational challenges faced by the \(\Lambda \)CDM model also indicate that we might have to look beyond GR as the underlying theory of gravity. Unlike GR, whose field equations contain only up to second-order derivatives, the modified theories with higher derivative Ricci/Riemann tensor gravity models include higher derivatives. Therefore, one expects significant differences between GR and modified theories. Since there are many ways of modifying GR in the strong-gravity and cosmological distances, each model has unique features. This leads to the following crucial question: Are there a set of unique signatures that distinguish GR from modified gravity (MG) theories? This review discusses three aspects of MG theories: (1) Why do we need to consider MG theories? (2) How to modify GR? and (3) What are the observational consequences? The review is written in a pedagogical style with the expectation that it will serve as a useful reference for theorists and observers and those interested in bridging the divide between theory and observations.

广义相对论 (GR) 是通过先进的 LIGO 和先进的处女座探测器直接探测到双黑洞和双中子星合并产生的引力波来证明的。这些检测证实了 GR 的预测，并提供了存在恒星质量黑洞 (BH) 的第一个直接证据。然而，在 BHs 中心出现奇点表明 GR 是不适用的，因为奇点处的等效原理被破坏了。这些奇点存在的事实表明，GR 不可能是一个普遍的时空理论。在低能极限下，\(\Lambda\)所面临的理论和观测挑战CDM 模型还表明，我们可能不得不将 GR 视为基本的引力理论。与场方程最多只包含二阶导数的 GR 不同，具有更高导数的 Ricci/Riemann 张量引力模型的修正理论包括更高的导数。因此，人们预计 GR 和修正理论之间存在显着差异。由于在强引力距离和宇宙距离上有多种修改 GR 的方法，每个模型都有其独特的特征。这导致了以下关键问题：是否有一组独特的特征可以将 GR 与修正重力 (MG) 理论区分开来？本综述讨论了 MG 理论的三个方面：(1) 为什么我们需要考虑 MG 理论？（2）如何修改GR？(3) 观察结果是什么？这篇评论以教学风格撰写，期望它将为理论家和观察者以及那些有兴趣弥合理论与观察之间鸿沟的人提供有用的参考。