Modeling speech production and speech articulation is still an evolving research topic. Some current core questions are: What is the underlying (neural) organization for controlling speech articulation? How to model speech articulators like lips and tongue and their movements in an efficient but also biologically realistic way? How to develop high-quality articulatory-acoustic models leading to high-quality articulatory speech synthesis? Thus, on the one hand computer-modeling will help us to unfold underlying biological as well as acoustic-articulatory concepts of speech production and on the other hand further modeling efforts will help us to reach the goal of high-quality articulatory-acoustic speech synthesis based on more detailed knowledge on vocal tract acoustics and speech articulation. Currently, articulatory models are not able to reach the quality level of corpus-based speech synthesis. Moreover, biomechanical and neuromuscular based approaches are complex and still not usable for sentence-level speech synthesis. This paper lists many computer-implemented articulatory models and provides criteria for dividing articulatory models in different categories. A recent major research question, i.e., how to control articulatory models in a neurobiologically adequate manner is discussed in detail. It can be concluded that there is a strong need to further developing articulatory-acoustic models in order to test quantitative neurobiologically based control concepts for speech articulation as well as to uncover the remaining details in human articulatory and acoustic signal generation. Furthermore, these efforts may help us to approach the goal of establishing high-quality articulatory-acoustic as well as neurobiologically grounded speech synthesis.