Modified theories of gravity: Why, how and what?

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