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Several versions of Sinusoidal+Residual analysis/synthesis models have been developed for music applications. They have been very successful and are already found in commercial and experimental tools used by musicians as well as researchers. In this paper, we begin by presenting the principles of this of this now classical model. However, the standard version of the model suffers from limitations in various cases. We discuss some improvements of the standard method designed in order to overcome these difficulties. We then present and compare other analysis techniques which use Elementary Waveforms, i.e. waveforms localised both on the frequency and the time axis. In particular, the High Resolution Matching Pursuit algorithm is proposed as a potentially successful new direction of research.