Pulsars
Pulsars are stellar corpses. No longer visible to the eye as a fiery sphere like the Sun, but small, rapidly spinning and relentlessly pulsing in radio waves. Pulsars are formed during cataclysmic events called "supernovae", in which the core of a larger star collapses, releasing a huge amount of energy which blows off the outer layers of the star.
Pulsars are remarkable for their extreme physical characteristics. Their masses are not very different from that of the Sun, but whereas the Sun's radius is a hundred times that of the Earth, pulsars have radii of around 10 km. So their densities are enormous - similar to the density of an atomic nucleus. Pulsars are "neutron stars". A small cube of neutron-star material, the same size as a sugar cube, would weigh as much as a cube of sugar that's one kilometre on a side.
Because of their small radii, neutron stars can rotate very rapidly. The slowest radio pulsars rotate once every few seconds, but much more rapid rotation is possible - we see some which rotate every few milliseconds.
To be a pulsar, a neutron star must have a strong magnetic field and it must rotate rapidly. The combination of a strong magnetic field with rapid rotation creates high voltages (like a dynamo), and these voltages accelerate electrons to high energies around the pulsar. Somehow - the details of the process are poorly understood - this leads to emission of radio noise (much like the static you can pick up with a radio-receiver if you detune it). The radio emission of a pulsar is concentrated along its magnetic axis, a bit like a lighthouse beam. And as the pulsar rotates the beam sweeps around the sky; we see it only when (if) it points towards us.