The hardware implementation of artificial neural networks and their learning algorithms is a fascinating area of research with far-reaching applications. However, the mapping from an ideal mathematical model to compact and reliable hardware is far from evident. This paper presents an overview of various methods that simplify the hardware implementation of neural network models. Adaptations that are proper to specific learning rules or network architectures are discussed. These range from the use of perturbation in multilayer feedforward networks and local learning algorithms to quantization effects in self-organizing feature maps. Moreover, in more general terms, the problems of inaccuracy, limited precision, and robustness are treated.