<p>Fluorite-based ferroelectric materials are revolutionizing the application space of polar semiconductors. These materials leverage robust polarization of extremely thin films, compatibility with the silicon chip processing, and decades of manufacturing experience to enable a new generation of ferroelectric memory devices. As a new paradigm for ferroelectrics, understanding of phase transitions and the switching mechanism in fluorites is essential both for advancing applications and for fundamental science. In this article, we outline the recent progress that has been made to understand the relative phase stability, phase transition and order parameter coupling, ferroelectric switching through unique nucleation and growth processes, and how defects affect these phases and processes. The main challenges, opportunities, and next steps for leveraging these materials for next-generation devices are reviewed.</p> Graphical abstract <p></p>