This book centers around a dialogue between Roger Penrose and Emanuele Severino about one of most intriguing topics of our times, the comparison of artificial intelligence and natural intelligence, as well as its extension to the notions of human and machine consciousness. Additional insightful essays by Mauro D'Ariano, Federico Faggin, Ines Testoni, Giuseppe Vitiello and an introduction of Fabio Scardigli complete the book and illuminate different aspects of the debate. Although from completely different points of view, all the authors seem to converge on the idea that it is almost impossible to have real "intelligence" without a form of "consciousness". In fact, consciousness, often conceived as an enigmatic "mirror" of reality (but is it really a mirror?), is a phenomenon under intense investigation by science and technology, particularly in recent decades. Where does this phenomenon originate from (in humans, and perhaps also in animals)? Is it reproducible on some "device"? Do we have a theory of consciousness today? Will we arrive to build thinking or conscious machines, as machine learning, or cognitive computing, seem to promise? These questions and other related issues are discussed in the pages of this work, which provides stimulating reading to both specialists and general readers. The Chapter "Hard Problem and Free Will: An Information-Theoretical Approach" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.