Ferroelectric materials are known to be ideal materials for nonvolatile memory devices, owing to their two electrically switchable spontaneous polarization states. However, difficulties in scaling down devices with ferroelectric materials have hindered their practical applications and research. The discovery of ferroelectricity in fluorite-structured ferroelectrics has revived research on semiconductor devices based on ferroelectrics. With their scalability and established fabrication techniques, the performance of nanoscale electronic devices with fluorite-structured ferroelectrics is being rapidly developed. However, the fundamental physics behind the superior ferroelectricity is yet to be elucidated. From this Perspective, the status of research on fluorite-structured ferroelectrics and state-of-the-art semiconductor devices based on them are comprehensively reviewed. In particular, the fundamental physics of fluorite-structured oxides is critically reviewed based on a newly developed theory as well as on the classical theory on ferroelectrics. A perspective on the establishment of emerging semiconductor devices based on fluorite-structured ferroelectrics is provided from the viewpoint of materials science and engineering.