The excellent complementary metal-oxide-semiconductor compatibility and rich physicochemical properties of hafnia-based materials, in particular the unique ferroelectricity that surpasses of conventional ferroelectrics, make hafnia-based devices promising candidates for industrial applications. This Perspective examines the fundamental properties of hafnia-based materials relevant to neuromorphic devices, including their dielectric, ferroelectric, antiferroelectric properties, and the associated ultra-high oxygen-ion conductivity. It also reviews neuromorphic devices developed leveraging these properties, such as resistive random-access memories, ferroelectric random-access memories, ferroelectric tunnel junctions, and (anti)ferroelectric field-effect transistors. We also discuss the potential of these devices for mimicking synaptic and neuronal functions and address the challenges and future research directions. Hafnia-based neuromorphic devices promise breakthrough performance improvements through material optimization, such as crystallization engineering and innovative device configuration designs, paving the way for advanced artificial intelligence systems.