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One of the unsolved fundamental questions of modern astrophysics is the behaviour of matter at extreme densities and pressures, as found in the core of neutron stars. Over the past few years great progress has been made thanks to the dedicated X-ray timing telescope Neutron Star Interior Composition Explorer (NICER), accurately measuring for the first time the mass and radius of a neutron star. I will explain how these measurements are made and how we can use them to constrain the neutron star interior, combining them with the first groundbreaking gravitational wave detections of merging neutron stars. I will discuss how multimessenger detections of gravitational wave events with electromagnetic counterparts can play a crucial role in constraining dense matter behaviour over the next few years. Finally, I will discuss how we can use knowledge of the interior of neutron stars to answer some open questions in astrophysics.