Soft State Automata explains how spiking neural networks work but before the development of Soft State Automata some researchers were trying to figure out the same thing. These early attempts are significant because they show the disillusionment with artificial neural network approaches during the mid-1990's yet they did not seek to simulate neurons at the bio-physical level. These researchers were seeking something deeper.
Networks of Spiking Neurons: The Third Generation of Neural Network Models (April 1996) by Wolfgang Maass. This article also gives references to the earliest research in the field.
The book that put spiking neural networks on the map is:
Pulsed Neural Networks (1999) edited by Wolfgang Maass and Christopher M. Bishop
But since then and up to now not much of significance was accomplished as the researchers got stuck on just what the neural spikes really represented. In other words they got stuck on the coding of the neural spikes.