The breakthrough discovery of gravitational waves by LIGO and VIRGO Collaborations has opened a new avenue for understanding of some of the most fundamental aspects of the universe. In particular, several well-motivated extensions of the Einstein General Relativity and standard cosmology may now become testable in the strong gravity regime through the measurements of gravitational waves at current and future facilities worldwide. I will give a broad (and somewhat biased) overview of potential implications of those measurements for understanding the quantum nature of black holes, quantum fuzziness of space-time, dark matter and some properties of the Higgs boson and the associated cosmology.