We are trying to develop computationally useful models of speech which incorporate what we know about the nature of speech. Current HMM approaches to acoustic-phonetic modeling that deal with context-sensitivity using decision trees and Gaussian mixture densities ignore much of the regularity caused by the fact that some of the context-sensitivity is due to relatively slow movements of the articulators. We have been building a model of simple coarticulation, which can be seen as a trainable generalization of a synthesis-by-rule system of the Holmes/Mattingly/Shearme kind, or as a generalized articulatory synthesizer. The assumption that we use in our current HDM (Hidden Dynamic Model) work is that the acoustic speech pattern can be modeled as a sequence of underlying segments, each characterised by a target vector appropriate to the type of segment, and subject to a coarticulation process that "blurs" what would otherwise be a sequence of steady sounds. We perform the blurring at a more abstract level than the spectrogram, and the spectrum shapes are derived from this internal state via a (learnable) non-linear transformation. (The HDM can also be seen as a generalization of an MLP!) The hidden dynamic space emerges from doing the job of producing acoustic patterns from segmental specifications. We shall show how the HDM learns to approximate speech patterns, explain the state of our work, and point to possible avenues for development, including asynchronous boundaries and speaker modeling. We are especially interested in the possibility of implementing something more like the Gestural Model of Articulatory Phonology.