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The measurements of quantities providing information on the values of the fundamental physical constants bring together a wide variety of measurements in very different parts of physics in a unique way. Taken both separately and together these measurements provide stringent tests of theory. They also throw light on the question: `How well do we understand physics via measurements at the highest level of accuracy?' They also have important practical applications. In this way they can point the way to the inadequacies and strengths of our knowledge and be used to benefit mankind. The first thorough review of the measurements relevant to the determination of the values of fundamental physical constants was that of Birge in 1929, and the latest CODATA review by Mohr and Taylor was published in 2000. Over the intervening period most of the old textbook methods have either disappeared or been considerably refined. Many of them have been replaced by determinations based on developments in such diverse areas as, for example, quantum electrodynamics, solid-state physics, low-temperature physics and laser spectroscopy. These have improved our knowledge of the values of the fundamental constants by many orders of magnitude. In accordance with their role as the natural units of physics, many of the methods have already found important applications for both defining and maintaining the SI units. These provide the basic units for the measurements used in science, technology and everyday life. The measurements involved in the latest evaluation by the CODATA Task Group on Fundamental Physical Constants are discussed together with the likely developments in the next few years. The pace of the subject reflects the overall pace of physics and technology and this can be used as a guide to future developments.