Coordinated detection and interpretation of multiple messenger signals, namely electromagnetic radiation, cosmic rays, neutrinos, and gravitational waves, offer a rewarding way to study compact objects. Successful observations of the neutron star merger event, GW170817, and the potential high-energy neutrino source, blazar TXS 0506+056, marked the opening of the Multi-messenger Era. In this talk, we summarize the current understanding of the four types of messengers. By presenting numerical simulation of particle interaction and propagation in the vicinity of compact objects, we illustrate how high-energy neutrinos and gamma-rays probe non-thermal processes in magnetar-powered transients and in black hole jets. In the second half of the talk, we switch to an observer’s perspective and investigate analysis frameworks aiming to exploit data across wavelengths and messengers. We close the talk by outlooking the future of Multi-messenger Astrophysics, in light of upcoming facilities and new questions brought by recent observations.