Spiking neurons represent the latest generation of neural networks designed to be more biologically realistic than more traditional artificial neural networks. This book provides a hands-on historical perspective on the development of neural networks, and investigates state-of-the-art methods for designing spiking neural networks to solve complex engineering problems. In particular, the book discusses the trade-off between biological plausibility and computational complexity of the numerous alternative models for the electrical properties of the neuron membrane, the electro-chemical interactions at the synapse, and for implementing learning. Often there is a trade-off between the sizes of the networks that can be implemented, and the complexity of the individual neurons in the network. The book investigates the definite lack of a rationale for organising all the different models in a network sense. This investigation has culminated in the development of the fuzzy spiking neural network (FSNN), which utilises fuzzy logic as a rationale for the deployment of biological models within a spiking neural network.