Recent discovery of ferroelectricity in doped HfO2 has reignited research interest in the ferroelectric field-effect transistor (FeFET) as emerging embedded nonvolatile memory with the potential for neuro-inspired computing. This paper reviews two major aspects for its application in neuro-inspired computing: ferroelectric devices as multilevel synaptic devices and the circuit primitive design with FeFET for in-memory computing. First, the authors survey representative FeFET-based synaptic devices. Then, the authors introduce 2T-1FeFET synaptic cell design that improves its in situ training accuracy to approach software baseline. Then, the authors introduce the FeFET drain–erase scheme for array-level operations, which makes the in situ training feasible for FeFET-based hardware accelerator. Finally, the authors give an outlook on the future 3D-integrated 2T-1FeFET design.