Blue straggler stars are members of open or globular clusters that are brighter and bluer than the main sequence turnoff. Recent studies show that the majority of blue stragglers in old open clusters are formed through mass transfer from an evolved star onto a main-sequence companion, resulting in blue straggler-white dwarf binary systems. I will discuss recent HST UV observations of white dwarf companions to blue straggler stars. These observations have allowed us to measure precise masses and ages for these white dwarfs, and to construct detailed models of blue straggler formation pathways. Some of these results are surprising and present challenges to our current understanding of mass transfer theory. In addition, white dwarf cooling ages from these observations have enabled the first study of the rotational evolution of blue straggler stars. These results demonstrate that rotation may be a useful clock to understand formation rates and lifetimes of blue stragglers, as well as a way to detect new types of post-mass-transfer systems.