Based on a sinusoidal model, an analysis/synthesis technique is developed that characterizes audio signals, such as speech and music, in terms of the amplitudes, frequencies, and phases of the component sine waves. These parameters are estimated by applying a peak-picking algorithm to the short-time Fourier transform of the input waveform. Rapid changes in the highly resolved spectral components are tracked by using a frequency-matching algorithm and the concept of "birth" and "death" of the underlying sine waves. For a given frequency track, a cubic phase function is applied to the sine-wave generator, whose output is amplitude-modulated and added to sines for other frequency tracks. The resulting synthesized signal preserves the general wave form shape and is nearly perceptually indistinguishable from the original, thus providing the basis for a variety of applications including signal modification, sound splicing, morphing and extrapolation, and estimation of sound characteristics such as vibrato. Although this sine-wave analysis/synthesis is applicable to arbitrary signals, tailoring the system to a specific sound class can improve performance. A source/filter phase model is introduced within the sine-wave representation to improve signal modification, as in time-scale and pitch change and dynamic range compression, by attaining phase coherence where sinewave phase relations are preserved or controlled. A similar method of achieving phase coherence is also applied in revisiting the classical phase vocoder to improve modification of certain signal classes. A second refinement of the sine-wave analysis/synthesis invokes an additive deterministic/stochastic representation of sounds consisting of simultaneous harmonic and aharmonic contributions. A method of frequency tracking is given for the separation of these components, and is used in a number of applications. The sinewave model is also extended to two additively combined signals for the separation of simultaneous talkers or music duets. Finally, the use of sine-wave analysis/synthesis in providing insight for FM synthesis is described, and remaining challenges, such as an improved sine-wave representation of rapid attacks and other transient events, are presented.