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Optical photons are powerful carriers of quantum information, which can be delivered in free space by satellites or in fibers on the ground over long distances. Entanglement of quantum states over long distances can empower quantum computing, quantum communications, and quantum sensing. Quantum optical memories are devices designed to store quantum information in the form of stationary excitations, such as atomic coherence, and are capable of coherently mapping these excitations to flying qubits. Quantum memories can effectively store and manipulate quantum states, making them indispensable elements in future long-distance quantum networks. Over the past two decades, quantum optical memories with high fidelities, high efficiencies, long storage times, and promising multiplexing capabilities have been developed, especially at the single-photon level. In this review, we introduce the working principles of commonly used quantum memory protocols and summarize the recent advances in quantum memory demonstrations. We also offer a vision for future quantum optical memory devices that may enable entanglement distribution over long distances.