Neutron stars form in the aftermath of a supernova explosion. They are extremely dense and very small, about 5-16 kilometers in diameter. The reason why they do not become black holes is because the star they formed from was not massive enough to create such an effect. Pulsars are also neutron stars, only they spin very rapidly and emit short but strong bursts of energy. If one notices a pulsar in the night sky, it will look like an ordinary star that is simply flashing.

A Binary star system is one that contains two stars orbiting around a common center of mass larger than theirs. An eclipsing binary system is one that contains a large star and a smaller star orbiting it. This type of system produces either a brightening or occluding effect, depending on whether the smaller star enhances the larger star's brightness or occludes it; this depends on the position of the smaller star in its orbit.
An X-Ray binary system is made up of a normal, living star and a collapsed star, which could be a white dwarf, a black hole or a neutron star. If these two stars are close enough to each other, the collapsed star will begin to suck material away from the normal one. As the matter is sucked into the white dwarf, black hole or neutron star, an immense amount of heat is produced, which results in the emissions of x-rays.