The emergence of doped hafnium oxide (HfO₂)-based ferroelectric films has enabled highly scalable and silicon-compatible ferroelectric devices, opening new frontiers in neuromorphic and reservoir computing. Among these, ferroelectric field-effect transistors (FeFETs) are particularly promising due to their analog memory characteristics and unique polarization dynamics. These properties make FeFETs ideal candidates for artificial synapses in neuromorphic architectures, supporting deep neural networks and spiking neural networks based on leaky-integrate-and-fire (LIF) mechanisms. Beyond neuromorphic computing, FeFETs also play a crucial role in physical reservoir computing, leveraging their intrinsic nonlinear and history-dependent behavior for efficient real-time learning. This approach offers significant advantages for time-series processing and edge artificial intelligence (AI) applications, addressing the growing need for energy-efficient computing. This article explores the principles, key demonstrations, and future potential of FeFET-based neuromorphic and reservoir computing, highlighting their impact on next-generation AI hardware.