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The subspace approach in speech signal analysis is commonly associated with the deployment of the singular value decomposition (SVD), or equivalently the eigendecomposition, to reveal useful subspace information about the signal of interest. The general premise that information in speech signals is almost completely contained in a lower dimensional subspace of the measurement space underscores their principal role in detecting the desired signal subspace. These ideas, which have been vigorously researched for speech enhancement problems, inspire the notion of a signal subspace model. Signal subspace modelling, as developed in this thesis, generally relates to the representation of the speech signal in terms of the signal subspace information. The signal model is composed of a set of subspace trajectories, and these trajectories jointly characterize the subspace information of the signal under consideration. Relying on an important result on noisy measurement matrices, the notion of robustness in subspace classification is also established to facilitate the formulation of robust distortion measures.