Over 200 millisecond radio pulsars have been observed in globular clusters, motivating theoretical studies of the formation and evolution of these sources through stellar evolution coupled to stellar dynamics. The specific abundance of millisecond pulsars is an order of magnitude larger in clusters than in the Galactic field. How do so many pulsars form? In this talk, I will first demonstrate how we model millisecond pulsars in globular clusters using realistic cluster simulations. I will show the importance of electron-capture supernovae for neutron star retention, and how millisecond pulsar formation is greatly enhanced through dynamical interaction processes. In particular, I will present our latest N-body model for the cluster 47 Tucanae, where we demonstrate good agreement with observations, including a large number of detected radio pulsars; 47 Tuc is one of the most massive and densest globular clusters, making it especially challenging to model with detailed N-body simulations. Our cluster models also demonstrate the possibility of dynamically forming binary neutron stars and neutron star - black hole binaries in clusters. I will end the talk by showing how we can use a large set of models that are representative of the present-day Milky Way globular clusters to quantify the merger rates of compact binary mergers.