This Colloquium reviews the development of quantum coherence as a physical resource, focusing on its characterization, quantification, manipulation, dynamics, and applications. Quantum coherence, a fundamental feature of quantum mechanics, underlies phenomena such as quantum interference and entanglement, and is essential in quantum optics, information, and thermodynamics. Recent research has also explored its role in biological systems. Despite its importance, a rigorous theory of quantum coherence as a resource has only recently been developed. The Colloquium discusses the resource theory of quantum coherence, which is analogous to the theory of entanglement. It introduces constraints, operations, and resources, defining incoherent states and operations. Incoherent states are diagonal in a preferred basis, while incoherent operations preserve this structure. The theory also explores different classes of incoherent operations, including maximally incoherent operations (MIO), incoherent operations (IO), strictly incoherent operations (SIO), and others. Quantifying quantum coherence involves defining monotones and measures that satisfy specific postulates, such as nonnegativity, monotonicity, strong monotonicity, convexity, uniqueness for pure states, and additivity. These include measures like relative entropy of coherence, coherence quantifiers based on matrix norms, geometric coherence, and others. The Colloquium also discusses the connection between coherence and entanglement theory, highlighting their similarities and differences. The dynamics of quantum coherence are explored, including its freezing under certain operations and its behavior in non-Markovian evolutions. Applications of quantum coherence are discussed in various fields, such as quantum thermodynamics, algorithms, metrology, and biology. The Colloquium concludes with a summary of the current state of research and open questions in the theory of quantum coherence.This Colloquium reviews the development of quantum coherence as a physical resource, focusing on its characterization, quantification, manipulation, dynamics, and applications. Quantum coherence, a fundamental feature of quantum mechanics, underlies phenomena such as quantum interference and entanglement, and is essential in quantum optics, information, and thermodynamics. Recent research has also explored its role in biological systems. Despite its importance, a rigorous theory of quantum coherence as a resource has only recently been developed. The Colloquium discusses the resource theory of quantum coherence, which is analogous to the theory of entanglement. It introduces constraints, operations, and resources, defining incoherent states and operations. Incoherent states are diagonal in a preferred basis, while incoherent operations preserve this structure. The theory also explores different classes of incoherent operations, including maximally incoherent operations (MIO), incoherent operations (IO), strictly incoherent operations (SIO), and others. Quantifying quantum coherence involves defining monotones and measures that satisfy specific postulates, such as nonnegativity, monotonicity, strong monotonicity, convexity, uniqueness for pure states, and additivity. These include measures like relative entropy of coherence, coherence quantifiers based on matrix norms, geometric coherence, and others. The Colloquium also discusses the connection between coherence and entanglement theory, highlighting their similarities and differences. The dynamics of quantum coherence are explored, including its freezing under certain operations and its behavior in non-Markovian evolutions. Applications of quantum coherence are discussed in various fields, such as quantum thermodynamics, algorithms, metrology, and biology. The Colloquium concludes with a summary of the current state of research and open questions in the theory of quantum coherence.