The force of gravity on the surface of a neutron star is about one hundred billion times greater than that on Earth's surface. Such a force would easily crush a human being. Material falling into the strong gravitational field of a neutron star acquires a great amount of energy and is heated to a temperature comparable to that in the deep interior of our sun, about 10 million degrees Fahrenheit. At this temperature matter emits most of its energy as X-rays. These X-rays can be detected and studied by satellites placed above Earth's X-ray absorbing atmosphere.
Here's what a neutron star might look like if you could crack it open:
At it's center the neutron star has a density comparable to that of an atomic nucleus. Recal that atoms are mostly comprised of empty space, with all the mass contained in the tiny nucleus. In this way the neutron star is somewhat like an enormous, macroscopic nucleus.
The study of neutron stars is one of the main goals of NASA's Rossi X-ray Timing Explorer (RXTE). Renamed shortly after its launch in December, 1995 in honor of Bruno Rossi, one of the pioneers of American X-ray astronomy, RXTE was designed to revolutionize the study of X-ray signals from neutron stars. Because of the large X-ray collecting area of its instruments, in particular the proportional counter array (PCA), which is the largest X-ray detector yet flown in space, and its capability to measure small changes in X-ray signals over times as short as a few millionths of a second, it has opened up an entirely new window for astronomers studying neutron stars and other astronomical X-ray sources as well.
If you are curious about recent breakthroughs in our understanding of neutron stars you can read about them in a review article entitled "New Views of Neutron Stars".