Quantum cryptography (QC) is poised to be the first commercial application of quantum mechanics at the individual quantum level. This review article, authored by Nicolas Gisin, Grégoire Ribordy, Wolfgang Tittel, and Hugo Zbinden, covers the rapid progress in both theory and experiments over recent years, emphasizing open questions and technological challenges. The article is structured into several sections: 1. **Introduction**: Discusses the historical context of quantum mechanics and its potential impact on modern cryptography, highlighting the intersection of quantum mechanics with information theory and the tension between quantum mechanics and relativity. 2. **A Beautiful Idea**: Explains the fundamental intuition behind QC, which involves using indivisible quanta and entangled systems to ensure secure communication. The basic idea is illustrated through the BB84 protocol, which uses non-orthogonal states to prevent eavesdropping. 3. **Technological Challenges**: Addressing the practical implementation of QC, including the sources of photons and the challenges of error correction and privacy amplification. 4. **Experimental Quantum Cryptography with Faint Laser Pulses**: Describes the use of weak laser pulses to implement QC, focusing on the Quantum Bit Error Rate (QBER) and the polarization entanglement. 5. **Experimental Quantum Cryptography with Photon Pairs**: Explores the use of photon pairs, including polarization entanglement and energy-time entanglement, and their applications in phase-coding, phase-time coding, and quantum secret sharing. 6. **Eavesdropping**: Discusses the problems and objectives of eavesdropping, including the intercept-resend strategy and the need for error correction and privacy amplification to ensure security. 7. **Conclusion**: Summarizes the key points and future directions in the field of quantum cryptography. The article emphasizes the interdisciplinary nature of QC, requiring contributions from physicists, computer scientists, and mathematicians. It also highlights the importance of classical information theory in the practical implementation of QC protocols, such as error correction and privacy amplification.Quantum cryptography (QC) is poised to be the first commercial application of quantum mechanics at the individual quantum level. This review article, authored by Nicolas Gisin, Grégoire Ribordy, Wolfgang Tittel, and Hugo Zbinden, covers the rapid progress in both theory and experiments over recent years, emphasizing open questions and technological challenges. The article is structured into several sections: 1. **Introduction**: Discusses the historical context of quantum mechanics and its potential impact on modern cryptography, highlighting the intersection of quantum mechanics with information theory and the tension between quantum mechanics and relativity. 2. **A Beautiful Idea**: Explains the fundamental intuition behind QC, which involves using indivisible quanta and entangled systems to ensure secure communication. The basic idea is illustrated through the BB84 protocol, which uses non-orthogonal states to prevent eavesdropping. 3. **Technological Challenges**: Addressing the practical implementation of QC, including the sources of photons and the challenges of error correction and privacy amplification. 4. **Experimental Quantum Cryptography with Faint Laser Pulses**: Describes the use of weak laser pulses to implement QC, focusing on the Quantum Bit Error Rate (QBER) and the polarization entanglement. 5. **Experimental Quantum Cryptography with Photon Pairs**: Explores the use of photon pairs, including polarization entanglement and energy-time entanglement, and their applications in phase-coding, phase-time coding, and quantum secret sharing. 6. **Eavesdropping**: Discusses the problems and objectives of eavesdropping, including the intercept-resend strategy and the need for error correction and privacy amplification to ensure security. 7. **Conclusion**: Summarizes the key points and future directions in the field of quantum cryptography. The article emphasizes the interdisciplinary nature of QC, requiring contributions from physicists, computer scientists, and mathematicians. It also highlights the importance of classical information theory in the practical implementation of QC protocols, such as error correction and privacy amplification.