Physical implementation of the memristor at industrial scale sparked the interest from various disciplines, ranging from physics, nanotechnology, electrical engineering, neuroscience, to intelligent robotics. As any promising new technology, it has raised hopes and questions; it is an extremely challenging task to live up to the high expectations and to devise revolutionary and feasible future applications for memristive devices. The possibility of gathering prominent scientists in the heart of the Silicon Valley given by the 2011 International Joint Conference on Neural Networks held in San Jose, CA, has offered us the unique opportunity of organizing a series of special events on the present status and future perspectives in neuromorphic memristor science. This book presents a selection of the remarkable contributions given by the leaders of the field and it may serve as inspiration and future reference to all researchers that want to explore the extraordinary possibilities given by this revolutionary concept.