Understanding their equation of state is one of the main reasons to study neutron stars. An important class in this search are the neutron star low mass X-ray binaries. I will give an overview of various observational methods used and discuss the problems encountered in determining the composition of neutron stars from low mass X-ray binaries only. I will show that a new and promising way forward is the study of accreting millisecond X-ray pulsars, systems very similar to the low mass X-ray binaries.