The coherent superposition of states, in combination with the quantization of
observables, represents one of the most fundamental features that mark the
departure of quantum mechanics from the classical realm. Quantum coherence in
many-body systems embodies the essence of entanglement and is an essential
ingredient for a plethora of physical phenomena in quantum optics, quantum
information, solid state physics, and nanoscale thermodynamics. In recent
years, research on the presence and functional role of quantum coherence in
biological systems has also attracted a considerable interest. Despite the
fundamental importance of quantum coherence, the development of a rigorous
theory of quantum coherence as a physical resource has only been initiated
recently. In this Colloquium we discuss and review the development of this
rapidly growing research field that encompasses the characterization,
quantification, manipulation, dynamical evolution, and operational application
of quantum coherence.