Over last six years, the LIGO-Virgo detections of gravitational waves from compact binary mergers have underlined their promise as an independent and powerful tool to explore the Universe. Nevertheless, the electromagnetic observations of the counterparts of gravitational-wave sources provide different and complementary information about the binary systems, and therefore the combination of `multimessengers' is expected to lead to significantly enhanced science outcomes. In this talk, I will highlight several promising measurements in cosmology and nuclear physics from LIGO-Virgo observations. I will then discuss the challenges and future aspects in these areas.