20 years in conception and 15 in construction, the SpiNNaker project has delivered the world's largest neuromorphic computing platform incorporating over a million ARM mobile phone processors and capable of modelling spiking neural networks of the scale of a mouse brain in biological real time. This machine, hosted at the University of Manchester in the UK, is freely available under the auspices of the EU Flagship Human Brain Project. This books tells the story of the origins of the machine, its development and its deployment, and the immense software development effort that has gone into making it openly available and accessible to researchers and students the world over. It also presents exemplar applications from 'Talk', a SpiNNaker-controlled robotic exhibit at the Manchester Art Gallery as part of 'The Imitation Game', a set of works commissioned in 2016 in honour of Alan Turing, through to a way to solve hard computing problems using stochastic neural networks. The book concludes with a look to the future, and the SpiNNaker-2 machine which is yet to come.