In this chapter, we introduce devices based on ferromagnetic or ferroelectric materials, their application in memory technologies, and their potential for neuromorphic computing applications. We will highlight the state of the art in magnetic and ferroelectric memories and the perspectives of development considering recent advances in material design and novel functionalities. In the case of ferromagnets, the basics of spintronics devices, exploiting both the charge and spin degrees of freedom of the electron, will be introduced. The three basic magnetic memory functionalities, reading, writing, and storing information will be described in the context of the physical processes that make them possible. The current challenges concerning the development of novel magnetic memory technologies as well as new approaches to overcome these difficulties will also be presented. In particular, promising concepts such as controlling magnetization switching using electric fields or pure spin currents will be introduced. For the ferroelectrics, the challenges of finding a suitable material that can be integrated into a complementary metal-oxide-semiconductor (CMOS) process with only small additional effort is the starting point of the discussion. It is illustrated that ferroelectric hafnium oxide solves many of the integration issues known from ferroelectrics having the perovskite structure. The embodiments and both challenges and potential of the three main ferroelectric memory concepts, namely, capacitor-based ferroelectric random-access memories, ferroelectric field effect transistors, and ferroelectric tunneling junctions, are then described. This chapter also presents the perspectives of using basic ferromagnetic and ferroelectric devices for beyond von Neumann and neuromorphic computing applications. First, approaches to use ferroelectric field effect transistors and magnetic tunnel junctions in logic-in-memory applications are described. Then, toward brain-inspired applications, it is shown how the switching dynamics of adequately patterned magnetic junctions and scaled ferroelectric field effect transistors can be used to realize important functions of synapses and neurons. Finally, an insight is given of how remaining and intrinsic imperfections can be leveraged for specific applications.