Neutron stars (NS) have been touted as laboratories for studying matter at extreme density since their discovery more than 50 years ago. I will describe how advances in theory, simulations, and experiments are finally allowing us to interpret of recent x-ray observations of NSs in terms of fundamental physics of high density matter. After a brief introduction to the phases of dense matter at supra nuclear density I will discuss the equation of state of dense neutron-rich matter and its relation to the the neutron star radius and properties of neutron-rich nuclei. In addition, I will discuss theoretical interpretation of observed transient thermal phenomena in accreting NSs and its implications for thermal and transport properties at extreme density and relatively low temperature.