The subject of this chapter is the estimation, representation, modification and use of spectral envelopes in the context of sinusoidal additive+residual analysis–synthesis. A spectral envelope is a function giving amplitude versus frequency, which is the envelope of a short-time spectrum. Even though the term spectral envelope is commonly used for the envelope of the magnitude of the STS only, we also consider envelopes for the phase of the STS, and even for the frequency of nearly-harmonic partials as a function of their harmonic number. One of the main features of spectral envelopes is that several important properties of sounds are captured in a simple and powerful representation. The concept of spectral envelope is connected with the production models (signal models and physical models) of musical instruments as well as with the perception of musical sounds. Spectral envelopes also offer a simple and concise representation of important sound properties which largely ease the control of synthesis models for musical applications. From the analysis viewpoint, the interest of spectral envelopes relies on the existence of many envelope estimation techniques. Spectral envelopes can be coded in one of several representations which differ by the memory space and the computation power they require. In his chapter, transcoding and manipulation of spectral envelopes are explained, as well as the use of spectral envelopes for the synthesis of sinusoidal and of non-sinusoidal parts of the signal. Some examples of spectral envelope applications for additive+residual analysis and synthesis, in various contexts and software systems, are given. Finally, a few conclusions and perspectives for future development and research concerning spectral envelopes in musical sound signal synthesis are proposed.