The study of compact objects such as black holes and neutron stars is an important component of modern astrophysics. Recent detections of astrophysical neutrinos, gamma-rays, ultrahigh energy cosmic rays, and gravitational waves open up opportunities to study compact objects with multi-messengers. In this talk, we first review the latest progress in Astroparticle Physics, including some surprising puzzles revealed by new observations. We demonstrate that the key to Multi-messenger Astrophysics is to understand and establish the link between the messengers. We then illustrate how to reach this goal from both theoretical and observational perspectives. From the theoretical side, we show that high-energy neutrinos and gamma-rays together may play an important role in understanding non-relativistic shock-powered transients. From the observational side, we investigate analysis frameworks aiming to exploit data across multiple wavelengths and messengers.