Abstract: Stars serve as the foundational components of astrophysics, with approximately half of them existing in binary systems. Understanding the evolution of these binaries is crucial for understanding mysterious phenomena from the existence of blue straggler stars to the diversity of explosive transients, to black-hole and neutron-star mergers. Modeling these observables needs state-of-the-art modeling of stars and their interactions. An exciting new modeling paradigm is exemplified in POSYDON, a cutting-edge publicly available binary population synthesis code, employs detailed stellar structure and binary simulations from MESA. The code balances both speed and accuracy, providing the best of both worlds and better serving the gravitational wave data analysis. In this presentation, I also delve into how binary stars are modeled in this framework and discuss key mechanisms in developing the new version of POSYDON: wind Roche-lobe overflow and the impact of magnetic braking on angular momentum evolution in binaries.