Observations of neutron stars are raising expectations that the mass-radius relation, and therefore, the equation of state of dense matter, might be determined. In a nutshell, the two most significant measurements would be an accurate determination of the neutron star radius and a tighter bound for the neutron star maximum mass. Each quantity sheds important information about the equation of state: the radius is closely related to the isospin properties of dense matter, and the maximum mass sets bounds to the densities achievable in compact stars and, hence, the composition (including the possibility that strange quark matter exists). Analytic solutions of Einstein's equations are useful in understanding these relationships. The impact of recent X-ray and optical observations of neutron stars (thermal emissions and QPOs) will be summarized.