Along with the iconic discovery of gravitational waves in 2015, the observation of numerous mergers of binaries of black holes and/or neutron stars have opened up a novel avenue to probe gravity at unprecedented scales and to test Einstein's general theory of relativity. It is however possible that the merging black hole-like objects are not really black holes but exotic alternatives mimicking black holes. The gravitational-wave signal from the merger of a regular compact binary can be modelled, and the analysis of data proceeds given that the models are accurate. There can be several unmodelled features in case the black holes are replaced by exotic objects. This project makes use of unmodelled methods together with modelled data analysis to optimally extract any exotic behaviour in these mergers. Such methods may give the first hint beyond Einstein's general relativity from gravitational-wave observations in the upcoming observing runs of the LIGO-Virgo-KAGRA experiments.