Neutron stars are truly marvelous objects. They represent the end result of the evolution of very massive stars and are the “left-overs” of the enormous explosion that accompanies the death of these stars – namely, a supernova explosion. In a radius of a dozen of kilometers only, these stars can accumulate as much mass as twice that of the Sun, reach temperatures of tens of millions of degrees and magnetic fields that millions of billions larger than those on Earth. More importantly, by being so compact, these stars produce enormous gravitational fields, the largest gravitational fields for an object with a hard surface. This chapter will explain how neutron stars have been discovered and how we have learnt about their incredible properties. It will also stress that, although we now know quite a lot about neutron stars, they still represent a significant mystery in physics, since we have only a rather vague idea of what is inside neutron stars and how they can be built in nature.