With his “physiologically oriented, dynamic model of the tongue, Joseph Perkell introduced in 1974 a new methodological approach to understanding the “relationships among phonetic models and the properties and capabilities of the speech-production mechanism.” This approach has guided a large part of our studies in the two last decades. In order to investigate how mechanical properties of the orofacial motor system constrain the degrees of freedom of speech articulation and contribute to shaping the speech signals exchanged between speakers and listeners, we, among other research groups, have developed increasingly more realistic 2D, and then 3D, finite element(FE) biomechanical models of the human vocal tract and face. After summarizing some of our modeling and simulation results that shed light on some basic characteristics of speech production, we present recent developments which aim to improve the realism of the models: evaluation of the links between the FE mesh structure (based either on tetrahedra, hexahedra, or mixed elements) and simulation accuracy; development of an active 3D element that simulates muscle mechanics and muscle force generation mechanisms; use of Diffusion Tensor Imaging to investigate muscle anatomy; design of an Atlas-based method (i.e., without manual image segmentation) for the automatic generation of subject-specific models.