  A remarkable fact about spherically-symmetric neutron stars in hydrostatic
equilibrium - the so-called Schwarzschild stars - is that the only physics that
they are sensitive to is the equation of state of neutron-rich matter. As such,
neutron stars provide a myriad of observables that may be used to constrain
poorly known aspects of the nuclear interaction under extreme conditions of
density. After discussing many of the fascinating phases encountered in neutron
stars, I will address how powerful theoretical, experimental, and observational
constraints may be used to place stringent limits on the equation of state of
neutron-rich matter.
