This review describes an emerging field of waveguide quantum electrodynamics (WQED) studying interaction of photons propagating in a waveguide with localized quantum emitters. In such systems, atoms and guided photons are hybridized with each other and form polaritons that can propagate along the waveguide, contrary to the cavity quantum optics setup. Emerging in such a system collective light-atom interactions result in super- and sub-radiant quantum states, that are promising for quantum information processing, and give rise to peculiar quantum correlations between photons. The review is aimed at both experimentalists and theoreticians from various fields of physics interested in the rapidly developing subject of WQED. We highlight recent groundbreaking experiments performed for different quantum platforms, including cold atoms, superconducting qubits, semiconductor quantum dots, quantum solid-state defects and at the same time provide a comprehensive introduction into various theoretical techniques to study atom-photon interactions in the waveguide.
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