Neutron stars are compact remnants of supernova explosions. They have radii of 11-13 km
and masses comparable to that of the sun. One could expect neutron stars to be quiet, dead
remnants of stellar evolution. Instead, they happen to produce most spectacular, extreme
radiative phenomena. This talk will give a broad overview of neutron star activity and recent
progress in understanding its mechanisms. Neutron stars generate powerful beams of coherent
radio waves, pulsed high-energy gamma-rays, relativistic electron-positron winds, and giant
X-ray flares. Some neutron stars live in binary systems and eventually merge, emitting strong
gravitational waves and creating explosions observed from cosmological distances. Recent
observational discoveries will be discussed, including the exciting detection of gravitational
waves from a neutron star merger and its electromagnetic counterpart.