The rapid expansion of artificial intelligence (AI) is driven by the explosion of data from sensors and edge devices, with global data expected to reach 175 zettabytes by 2025. This demand necessitates highly efficient computing systems. To address these challenges, post-complementary metal-oxide-semiconductor (Post-CMOS) technologies, such as memristor-based hardware, offer promising solutions for neuromorphic computing. However, issues with material properties, device reliability, and standardization hinder the commercialization of memristor-based devices. In this context, ferroelectric materials emerge as a potential breakthrough for neuro-inspired AI chips. These materials, particularly those in the perovskite oxide family, offer nonvolatile, energy-efficient solutions with fast switching speeds, low power consumption, and small form factors. Ferroelectric synapses, implemented in devices such as ferroelectric field-effect transistors (FeFETs) and ferroelectric tunnel junctions (FTJs), provide superior performance by utilizing polarization states for weight modulation in artificial neural networks that mimic biological synapses. Additionally, the flexibility of ferroelectric polymers enables low-cost, scalable, and wearable devices. The future of memory technology holds immense promise, with ferroelectric materials offering significant potential for the development of efficient, low-energy AI chips designed for brain-inspired computing. These materials have the capacity to revolutionize neuromorphic computing; however, overcoming challenges in material optimization and device engineering is crucial to making ferroelectric devices practical and reliable synaptic elements.