The final compact remnants of massive stars, neutron stars and black holes, were first predicted theoretically in the beginnings of the 20th century, and observational evidence for their existence has accumulated steadily over the past 40 years. Nevertheless, our physical understanding of their formation remains incomplete and paradigms are still being challenged as quantitative analyses of observed systems harboring such compact objects become possible. In this talk I will summarize both our basic understanding of their formation and highlight some of the recent challenges and questions we are facing. I will further discuss the ultimate fate of neutron stars and black holes when found in close binary systems leading to most energetic mergers. Such mergers not only are thought to power explosions in gamma-rays but are also expected to release immense amounts of energy in gravitational waves. I will review our current efforts targeting the direct detection of gravitational waves, our expectation for detection rates, and the prospects for advancing multi- messenger astronomy in the near future.