Appears in collection : Balzan Conference on Open Issues in Gravitation

Six months ago, a new gravitational-wave transient catalogue was released by the LIGO, Virgo and KAGRA collaborations. As the worldwide network of gravitational-wave detectors continues to increase in sensitivity, the quantity and quality of the detected signals from compact binary coalescences also increases. In this presentation I will briefly explore various tests applied in the analysis of recent gravitational-wave observations, to see how well these match the predictions from General Relativity. First are consistency tests between the observed signal and theoretical predictions that describe the strong-field dynamics of spacetime present during binary mergers. These are followed by a set of tests that examine the nature of gravitational waves and the propagation characteristics of these signals. Finally, a suite of tests are discussed that probe the fundamental properties of the coalescence remnants with the observed gravitational waves.