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The merging of continuous wave laser-based precision optical-frequency metrology with mode-locked ultrafast lasers has led to precision control of the visible and near-infrared frequency spectrum produced by mode-locked lasers. Such a phase-controlled mode-locked laser forms the foundation of a "femtosecond optical-frequency comb generator" with a regular comb of sharp lines with well-defined frequencies. For a comb with sufficiently broad bandwidth, it is now straightforward to determine the absolute frequencies of all of the comb lines. This ability has revolutionized optical-frequency metrology, synthesis, and optical atomic clocks. Precision femtosecond optical-frequency combs also have a major impact on time-domain applications, including carrier-envelope phase stabilization, synthesis of a single pulse from two independent lasers, nonlinear spectroscopy, and passive amplifiers based on empty external optical cavities. The authors first review the frequency-domain description of a mode-locked laser and the connection between the carrier-envelope phase and the frequency spectrum to provide a basis for understanding how the absolute frequencies can be determined and controlled. Using this understanding, applications in optical-frequency metrology and synthesis and optical atomic clocks are discussed. This is followed by discussions of time-domain experiments.