A continuous exponential rise has been observed in the storage and processing of the data that may not curtail in the foreseeable future. The required data processing speed and power consumption are restricted by the buses between the logic and memory devices that are characteristic of the von Neumann computing architecture. Bio-mimicking neuromorphic computing has garnered considerable academic and industrial interest to resolve these challenges. Additionally, devices based on emerging nonvolatile memories capable of mimicking the behaviors of synapses and neurons, which are the main elements in biological computing systems (brains), are attracting significant interest from the device community. With the discovery of ferroelectricity in fluorite-structured oxides, such as HfO₂ and ZrO₂, which are compatible with the state-of-the-art complementary-metal-oxide-semiconductor processes, ferroelectric devices have rapidly evolved as the main direction of these research and development activities. Fundamental science related to fluorite-structured ferroelectrics has been intensively studied over the last decade. At present, the focus is gradually moving to practical applications, including neuromorphic computing and advanced classical processing or memory units in the conventional von Neumann architecture. However, despite its rapid development, the wealth of recent progress in neuromorphic computing devices based on fluorite-structured ferroelectrics has not been reviewed and systemized. This progress report comprehensively reviews and systemizes the recent progress in artificial synaptic and spiking neuron devices for neuromorphic computing based on fluorite-structured ferroelectrics. (Figure presented.).