Glottal inverse filtering is a technique used to derive the glottal waveform during voiced speech. Closed phase inverse filtering (CPIF) is a common approach for achieving this goal. During the closed phase there is no input to the vocal tract and hence the impulse response of the vocal tract can be determined through linear prediction. However, a number of problems are known to exist with the CPIF approach. This review paper briefly details the CPIF technique and highlights certain associated theoretical and methodological problems. An overview is then given of advanced methods for inverse filtering: model based, adaptive iterative, higher order statistics and cepstral approaches are examined. The advantages and disadvantages of these methods are highlighted. Outstanding issues and suggestions for further work are outlined. © Springer-Verlag Berlin Heidelberg 2005.