Optical quantum memory is crucial for quantum information processing, serving as a synchronization device, identity quantum gate, and tool for converting heralded photons to photons-on-demand. It is essential for quantum computing and long-distance quantum communication via quantum repeaters. The paper reviews the state-of-the-art in optical quantum memory, including performance criteria and current achievements. Quantum memory stores a quantum state represented by a density matrix ρ and outputs a state ρ', which should be close to ρ. The ultimate performance criterion is the worst-case fidelity, defined by F(ρ) = Tr√(√ρ'ρ√ρ'). A threshold fidelity allows fault-tolerant quantum error correction to overcome memory imperfections. Performance criteria include fidelity, efficiency, transfer coefficient, and conditional variance. Multimode capacity determines the number of optical modes that can be stored, and storage time is another essential criterion. Applications of optical quantum memory include quantum computation, quantum communication, precision measurements, and single-photon sources. In quantum communication, quantum repeaters enable long-distance communication by storing and retrieving quantum information. In precision measurements, quantum memory reduces quantum noise, improving the accuracy of magnetometry, clocks, and spectroscopy. The paper discusses various optical quantum memory implementations, including optical delay lines, cavities, electromagnetically-induced transparency (EIT), photon-echo, and off-resonant Faraday interaction. EIT-based memory stores light by slowing it down and transferring its quantum state into collective atomic excitation. Photon-echo memory uses inhomogeneous broadening to rephase atomic dipoles and re-emit the stored signal. Off-resonant Faraday interaction stores quantum information in the polarization of light by utilizing the interaction between light and atoms. The DLCZ protocol creates long-lived, long-distance entanglement between atomic ensembles, enabling quantum repeaters. Photon-echo quantum memory, based on controlled reversible inhomogeneous broadening (CRIB), allows efficient storage and retrieval of quantum information. Atomic frequency combs (AFC) enable multi-mode storage with high efficiency. Off-resonant Faraday interaction provides a method for storing quantum information in the polarization of light. The paper highlights the importance of optical quantum memory in quantum information processing and reviews the latest advancements in the field, including experimental demonstrations and theoretical models.Optical quantum memory is crucial for quantum information processing, serving as a synchronization device, identity quantum gate, and tool for converting heralded photons to photons-on-demand. It is essential for quantum computing and long-distance quantum communication via quantum repeaters. The paper reviews the state-of-the-art in optical quantum memory, including performance criteria and current achievements. Quantum memory stores a quantum state represented by a density matrix ρ and outputs a state ρ', which should be close to ρ. The ultimate performance criterion is the worst-case fidelity, defined by F(ρ) = Tr√(√ρ'ρ√ρ'). A threshold fidelity allows fault-tolerant quantum error correction to overcome memory imperfections. Performance criteria include fidelity, efficiency, transfer coefficient, and conditional variance. Multimode capacity determines the number of optical modes that can be stored, and storage time is another essential criterion. Applications of optical quantum memory include quantum computation, quantum communication, precision measurements, and single-photon sources. In quantum communication, quantum repeaters enable long-distance communication by storing and retrieving quantum information. In precision measurements, quantum memory reduces quantum noise, improving the accuracy of magnetometry, clocks, and spectroscopy. The paper discusses various optical quantum memory implementations, including optical delay lines, cavities, electromagnetically-induced transparency (EIT), photon-echo, and off-resonant Faraday interaction. EIT-based memory stores light by slowing it down and transferring its quantum state into collective atomic excitation. Photon-echo memory uses inhomogeneous broadening to rephase atomic dipoles and re-emit the stored signal. Off-resonant Faraday interaction stores quantum information in the polarization of light by utilizing the interaction between light and atoms. The DLCZ protocol creates long-lived, long-distance entanglement between atomic ensembles, enabling quantum repeaters. Photon-echo quantum memory, based on controlled reversible inhomogeneous broadening (CRIB), allows efficient storage and retrieval of quantum information. Atomic frequency combs (AFC) enable multi-mode storage with high efficiency. Off-resonant Faraday interaction provides a method for storing quantum information in the polarization of light. The paper highlights the importance of optical quantum memory in quantum information processing and reviews the latest advancements in the field, including experimental demonstrations and theoretical models.