The structure of neutron stars is determined by the so-called TOV equations of general relativity. Knowledge of the pressure-energy density relation is sufficient to determine the neutron star mass-radius (M-R) relation. Recent observations from X-ray telescopes, radio timing of pulsars, and gravitational wave observations, have provided several constraints on the masses and radii of neutron stars. Major efforts are being devoted to inferring the underlying pressure-energy density relation, often called the equation of state (EOS), of dense matter.  This involves the inversion of the TOV relations.  The close correspondence between neutron star matter pressure near the saturation density and the radii of typical neutron stars is one example of a semi-universal relation relating the M-R relation to the EOS, as is the Yagi-Yunes I-Love relation connecting the moments of inertia and the tidal deformability of neutron stars. These relations are valid for all or nearly all equations of state to high precision. However, the inference of the EOS from mass and radius observations, which have appreciable uncertainties, is also dependent upon model dependences of the inversion method. This talk will review the structure and observations of neutron stars and will introduce several semi-universal relations relating the mass and radius directly to the central densities and pressures of the neutron star. One important result is an analytic method of inverting an individual M-R relation to its underlying EOS to within about 0.5%.