The central densities of neutron stars are the highest known in the Universe, so measurements probing the interiors of radio pulsars, or even their overall mass and radii, can give us unique insights into the physics of matter at extreme densities. The discovery of several interesting new pulsars as well as improved instrumentation has finally allowed us to start measuring the masses of the rapidly spinning millisecond pulsars. These systems have had potentially substantial amounts of mass accreted onto them in the past and are likely more massive, on average, than "canonical" 1.4 Msun neutron stars. Relativistic Shapiro Delay has been used to make very precise measurements of 1.67 and 1.97 Msun neutron stars in the past two years. These systems strongly constrain the equation of state of nuclear matter and a variety of other topics in physics/astrophysics. Finally, I'll show that there is good potential for more measurements in the near future.