There has been tremendous progress in the past few years on the measurements of masses of
neutron stars and black holes in our Galaxy. In this talk, I will discuss how applying statistical
techniques on the new data reveals the evolution of these compact objects and the dividing
line between them, while raising questions about our understanding of the supernova mechanism.
I will then present our recent measurements of the radii of neutron stars and a new formalism by
which these measurements can be used to study the neutron star interior. I will show how the
combination of the tightly constrained radii and the discovery of a two solar mass pulsar has allowed
for the first astrophysical inference of the pressure of cold matter above nuclear saturation density.
Finally, I will discuss the implications of these developments for nuclear theory and astrophysics.