This chapter explores the fundamental concepts, architectures, and applications of quantum computing, focusing on the essential role of quantum gates, circuits, and algorithms. Beginning with the theoretical underpinnings of quantum mechanics—superposition and entanglement—the chapter examines how these principles enable quantum gates such as Pauli-X, Hadamard, and CNOT to form the basis of quantum circuits. It discusses the design and operation of circuits, highlighting the importance of error mitigation and decoherence management. Furthermore, two landmark quantum algorithms are introduced: Shor’s algorithm, which revolutionises integer factorisation and poses challenges to classical cryptography, and Grover’s algorithm, which provides quadratic speedup in unstructured database searches. The chapter also reviews the state of quantum hardware, including superconducting and trapped-ion qubits, and reflects on milestones such as Google’s demonstration of quantum supremacy. Finally, practical applications and industry implications are discussed, including materials design, environmental modelling, logistics, finance, and cryptography. By bridging theoretical principles with practical advances, this chapter provides a comprehensive overview of quantum computing’s transformative potential and its challenges for real-world adoption.