Recent observations of neutron stars have yielded valuable insights into their structure and into the properties of the underlying dense matter equation of state. Studies of X-ray bursts have revealed quasi-periodic oscillations that seem to be associated with surface vibrational modes. In addition, there are new observations of x-ray thermal emission from globular cluster neutron stars. Together with pulsar timing measurements of neutron star masses and rotation periods, these observations can lead to constraints in the neutron star mass-radius plane. The implications for the dense matter equation of state will be explored.