This review provides a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. It discusses quantum noise spectra, weak continuous measurements, and the standard quantum limit (SQL) on linear amplifiers and position detectors. The SQL arises from the fundamental quantum mechanical constraints on the precision of measurements, particularly in the case of phase-preserving amplifiers. The review emphasizes the importance of quantum noise in determining the performance of detectors and amplifiers, and explores various methods for achieving quantum-limited measurements, including weak continuous measurements, back-action evasion, and feedback techniques. It also discusses the role of quantum noise in mesoscopic systems and its implications for quantum information processing. The review highlights the importance of understanding quantum noise in both theoretical and practical contexts, and provides a comprehensive overview of the current state of research in this area. The SQL is shown to be a fundamental limit that must be respected in any measurement or amplification process, and the review provides a detailed analysis of the conditions under which this limit can be achieved. The review also discusses the relationship between quantum noise and quantum measurement, and the implications of this relationship for the design and operation of quantum devices. The review concludes with a discussion of the practical considerations involved in achieving quantum-limited measurements, and the importance of these considerations in the development of quantum technologies.This review provides a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. It discusses quantum noise spectra, weak continuous measurements, and the standard quantum limit (SQL) on linear amplifiers and position detectors. The SQL arises from the fundamental quantum mechanical constraints on the precision of measurements, particularly in the case of phase-preserving amplifiers. The review emphasizes the importance of quantum noise in determining the performance of detectors and amplifiers, and explores various methods for achieving quantum-limited measurements, including weak continuous measurements, back-action evasion, and feedback techniques. It also discusses the role of quantum noise in mesoscopic systems and its implications for quantum information processing. The review highlights the importance of understanding quantum noise in both theoretical and practical contexts, and provides a comprehensive overview of the current state of research in this area. The SQL is shown to be a fundamental limit that must be respected in any measurement or amplification process, and the review provides a detailed analysis of the conditions under which this limit can be achieved. The review also discusses the relationship between quantum noise and quantum measurement, and the implications of this relationship for the design and operation of quantum devices. The review concludes with a discussion of the practical considerations involved in achieving quantum-limited measurements, and the importance of these considerations in the development of quantum technologies.