Over the past few years, quantum computers have captivated the popular imagination like never before, as tech giants such as Google, IBM, and Intel race to stake their claim on the first generation of programmable quantum computing hardware. However, while the long theorized quantum computer has indeed begun its transition from academic abstraction to commercial reality, there remains an enormous conceptual chasm between the glossy promises of quantum computing PR hype and the rigorous formal training of most undergraduate physicists. In this talk, I attempt to bridge that chasm. I present a broad and accessible introduction to the fundamentals of quantum information theory and current-generation quantum computing hardware, focusing in particular on the formalism of quantum bits, decoherence, error correction, and the design and fabrication of superconducting qubits.