Motivated by the opportunities presented for studies relevant to nuclear structure, astrophysics, and fundamental symmetries with nuclear beta decay, the Facility for Rare Isotope Beams (FRIB) Theory Alliance topical program "Future Directions in Nuclear Beta Decays at FRIB" was held in September of 2025. This white paper summarizes the main points of discussion over the two-week program, and it aims to provide a snapshot of the current status of the field while also highlighting important questions and opportunities for future work. We provide an overview of the experimental tools and techniques that enable modern beta decay studies, discuss the current state of nuclear many-body approaches used to study beta decays, and highlight the important science questions that can be addressed by weak decays.