Neuromorphic engineering represents one of the most promising computing paradigms for overcoming the limitations of the present-day computers in terms of energy efficiency and processing speed. While traditional neuromorphic circuits are based on complementary metal oxide semiconductor (CMOS) transistors and large capacitors, the recently emerging nanoelectronic devices stand out as promising candidates for building the fundamental neuromorphic elements: neurons and synapses. In this chapter, we illustrate how hafnium oxide-based ferroelectric field-effect transistors (FeFETs) can be used to realize both artificial neurons and synapses for spiking neural networks. In particular, the accumulative switching property of FeFETs will be exploited to mimic the integrate-and-fire neuronal functionality, whereas the continuously tunable synaptic weights and the plasticity will be implemented by the partial polarization switching in large-area devices. Finally, the use of FeFETs for deep neural networks will be briefly discussed.