Due to the voltage driven switching at low to moderate voltages combined with a nonvolatile behavior of the achieved polarization state, ferroelectric materials have a unique potential for a wide class of low power nonvolatile electronic devices. However, for many years, the competitivity of such devices was hindered by the compatibility issues of well-known ferroelectric materials based on perovskite crystals with established complementary metal oxide semiconductor technology. The discovery of ferroelectricity in hafnium oxide and related materials changed this situation and opened up a path towards scalable ferroelectric devices. The natural application of any nonvolatile device is as a memory cell in nonvolatile memories. However, the nonvolatile memory devices also built the basis for other applications like in-memory computing, nonvolatile logic or neuromorphic devices. Based on the readout mechanism three different basic ferroelectric devices can be constructed: ferroelectric capacitors, ferroelectric field effect transistors and ferroelectric tunneling junctions. In this article after an introduction first the material science of the ferroelectricity in hafnium oxide and related materials will be summarized with a special focus on tailoring the switching characteristics towards different nonvolatile applications. A summary of the current status of nonvolatile semiconductor memories using the three fundamental device architectures then lays the ground for looking into applications like in-memory computing or nonvolatile logic were the separation between memory function and switching function can be overcome. Finally a special focus will be given to showcase how the basic building blocks of spiking neural networks, the neuron and the synapse, can be realized using the basic ferroelectric devices and how they can be combined to realize neuromorphic computing systems. A summary, comparison with other technologies like resistive switching devices and finally an outlook complete the paper. This article is protected by copyright. All rights reserved.