Reverberation, a component of any sound generated in a natural environment, can degrade speech intelligibility or more generally the quality of a signal produced within a room. In a typical setup for teleconferencing, for instance, where the microphones receive both the speech and the reverberation of the surrounding space, it is of interest to have the latter removed from the signal that will be broadcast. A similar need arises for automatic speech recognition systems, where the reverberation decreases the recognition rate. More ambitious applications have addressed the improvement of the acoustics of theatres or even the creation of virtual acoustic environments. In all these cases dereverberation is critical. The process of recovering the source signal by removing the unwanted reverberation is called dereverberation. Usually only a reverberated instance of the signal is available. As a consequence only a blind approach, that is a more difficult task, is possible. In more precise terms, unsupervised or blind audio de-reverberation is the problem of removing reverberation from an audio signal without having explicit data regarding the system and the input signal. Different approaches have been proposed for blind dereverberation. A possible discrimination into two classes can be accomplished by considering whether or not the inverse acoustic system needs to be estimated. The aim of this work is to investigate the problem of blind speech dereverberation, and in particular of the methods based on the explicit estimate of the inverse acoustic system, known as “reverberation cancellation techniques”. The following novel contributions are proposed: the formulation of single and multichannel dereverberation algorithms based on a maximum likelihood (ML) approach and on the natural gradient (NG); a new dereverberation structure that improves the speech and reverberation model decoupling. Experimental results are provided to confirm the capability of these algorithms to successfully dereverberate speech signals.