Neutron stars are amongst the most compact and exotic objects in the universe. When born in pairs, their eventual merging is responsible for some of the most energetic phenomena and plays a significant role in the chemical evolution of galaxies. This thesis combines analytical calculations with observations of stellar abundances to gain further insight into how these binaries are formed and the nucleosynthesis that takes place once they eventually merge under the influence of gravitational radiation.

We derive a relation between key parameters governing the process of bringing neutron stars to separations at which they are able to merge within a Hubble time. We also examine the conditions at the onset of a stellar merger through detailed stellar modeling of an observed progenitor system. We utilize observed stellar abundances to place stringent constraints on the progenitor site of r-process nucleosynthesis and find it to be consistent with expectations from neutron star mergers. We further utilize these stellar abundances to place constraints on another proposed site of the r-process, namely the collapsar, and find the abundances to be in tension with theoretical predictions of the model. Finally, we use stellar abundances to make predictions of future electromagnetic transients to be detected from these mergers and to test their viability as an r-process production mechanism throughout cosmic time.