Computer technology has improved exponentially over the last fifty years. But the headroom for bigger and better electronic solutions is running out. Our best hope is to engage the power of quantum physics. "Quantum algorithms" had already been written long before hardware was built. These would enable, for example, a quantum computer to exponentially speed up an information search or crack the mathematical trick behind internet security. However, making a quantum computer is incredibly difficult. Despite hundreds of laboratories around the world working on them, we are only just seeing them come close to "supremacy," where they can outperform a traditional computer. In this approachable introduction to the subject, Brian Clegg explains algorithms and their quantum counterparts, explores the physical building blocks and quantum weirdness necessary to make a quantum computer, and uncovers the capabilities of the current generation of machines.