<i>Colloquium</i>: Measuring the neutron star equation of state using x-ray timing

How are two essential quantities of neutron stars (the mass and radius), which provide constraints for the equation of state in their interiors where supranuclear densities are experienced, precisely determined? This Colloquium discusses major techniques for how this information can be inferred from x-ray observations of neutron stars that accrete matter from a binary companion, or of isolated neutron stars that experience seismic vibrations, taking into account rotation, relativistic effects, and magnetic fields.