The rapid progress of the internet of things, cloud computing, and artificial intelligence has increased demand for high-performance computing. This demand has led to a focused exploration of novel nonvolatile memory (NVM) and brain-inspired neuromorphic-computing electronics, with research efforts directed at identifying materials compatible with complementary metal-oxide-semiconductor technology. Exploring fluorite-structured hafnium-zirconium oxide (HZO) mixed oxides has revealed promising ferroelectric (FE) and memristor characteristics, suggesting potential applications in emerging technologies. However, certain intrinsic properties of HZO-based FEs, such as high coercive fields (Ec) and polarization metastability, may pose challenges for commercial viability. Recent investigations of fluorite-structured HZO-based antiferroelectrics (AFEs) have highlighted their advantages, including lower energetic barriers, higher switching speeds, and a uniform phase distribution. These inherent benefits position fluorite-structured HZO-based AFEs as potential candidates within the NVM landscape. Furthermore, the accumulated polarization and spontaneous depolarization characteristics of fluorite-structured HZO-based AFEs make them worthy of potential integration into neuromorphic-computing because they resemble certain aspects of neuron behavior. Despite these positive aspects, a more thorough exploration and consideration are needed to address existing challenges. This review aims to present fluorite-structured HZO-based AFE materials and highlight the current challenges, possible applications, and future opportunities and can act as an update for recent developments in these intriguing materials and provide guidance for future researchers in the optimization and design of HZO-based AFE materials and devices for emerging NVM and neuromorphic-computing applications.