We live in an era of breakthrough discoveries in gravitational waves (GW) astronomy. Every month or so, such discoveries by LIGO/Virgo have been making headlines as these events' nature has been far from the expectations. But why are we puzzled? And what is the road ahead for us to understand these events? I discuss two of the puzzling events that LIGO has discovered: 1) The most massive binary black hole merger with masses above the pair-instability limit. After a deep dive into the physics of pair-instability supernova, I will discuss how a broader perspective on the host environment of binary black holes can hold the key to understand the nature of such massive systems. 2) The most massive binary neutron star merger. I will present possible scenarios on why we have not detected such systems in the radio observations before and how the key to understanding these events might lie in the r-process enrichment in the early universe and magnetic field evolution of neutron stars. Through these two examples, I will conclude that it is only through the synergy of astronomy with EM waves and astronomy with GWs, that we can achieve an unbiased perspective on the nature of these mysterious events.