Mimicking and replicating the function of biological synapses with engineered materials is a challenge for the 21st century. The field of neuromorphic computing has recently seen significant developments, and new concepts are being explored. One of these approaches uses topological defects, such as domain walls in ferroic materials, especially ferroelectrics, that can naturally be addressed by electric fields to alter and tailor their intrinsic or extrinsic properties and functionality. Here, we review concepts of neuromorphic functionality found in ferroelectric domain walls and give a perspective on future developments and applications in low-energy, agile, brain-inspired electronics and computing.