The colloquium by Alexander Streltsov, Gerardo Adesso, and Martin B. Plenio discusses the development of a rigorous theory of quantum coherence as a physical resource. Quantum coherence, a fundamental feature of quantum mechanics, is essential for various phenomena in quantum optics, quantum information, solid-state physics, and nanoscale thermodynamics. The authors review the progress in understanding and quantifying quantum coherence, including the characterization, quantification, manipulation, dynamical evolution, and operational applications of quantum coherence. They explore the resource theory of quantum coherence, which aims to identify the conditions under which coherence can be transformed into other resources, such as entanglement. The colloquium also covers the quantification of quantum coherence through various measures and monotones, the dynamics of coherence in open quantum systems, and the applications of quantum coherence in fields like quantum thermodynamics, quantum algorithms, and quantum metrology. The authors highlight the connections between quantum coherence and other nonclassical resources, such as asymmetry and entanglement, and discuss the challenges and open questions in the field.The colloquium by Alexander Streltsov, Gerardo Adesso, and Martin B. Plenio discusses the development of a rigorous theory of quantum coherence as a physical resource. Quantum coherence, a fundamental feature of quantum mechanics, is essential for various phenomena in quantum optics, quantum information, solid-state physics, and nanoscale thermodynamics. The authors review the progress in understanding and quantifying quantum coherence, including the characterization, quantification, manipulation, dynamical evolution, and operational applications of quantum coherence. They explore the resource theory of quantum coherence, which aims to identify the conditions under which coherence can be transformed into other resources, such as entanglement. The colloquium also covers the quantification of quantum coherence through various measures and monotones, the dynamics of coherence in open quantum systems, and the applications of quantum coherence in fields like quantum thermodynamics, quantum algorithms, and quantum metrology. The authors highlight the connections between quantum coherence and other nonclassical resources, such as asymmetry and entanglement, and discuss the challenges and open questions in the field.