Densities in neutron star cores can reach up to ten times the density of a normal atomic nucleus, and
the stabilising effect of gravitational confinement permits long-timescale weak interactions. This
generates matter that is neutron-rich, and opens up the possibility of stable states of strange matter,
something that can only exist in neutron stars. Our uncertainty about the nature of matter under these conditions is encoded in the Equation of State (EOS), which can be linked to macroscopic observables like mass, radius, tidal deformation or moment of inertia. I will review efforts to measure the EOS using electromagnetic observations of neutron stars. This is a major goal of current telescopes like NICER, as well as future facilities like the Square Kilometer Array and the proposed large area X-ray telescopes eXTP and Strobe-X.