This paper overviews our work on the links between coarticulation modeling, approached from the point of view of predicting the vocal tract shape from the phonetic sequence, and the available real-time MRI corpora. Real-time MRI has revolutionized the acquisition of articulatory data through the image quality, the possibility of acquiring and denoising the speech signal, and the possibility of recording corpora containing several thousand sentences. Coarticulation modeling is only possible with the ability to reliably track articulator contours in many images. Tracking techniques using neural networks have provided efficient solutions comparable in reliability to humans. Finally, we show that even if recurrent neural networks trained on these corpora can successfully predict the shape of the vocal tract, it is still necessary to use constraints directly from phonetics to ensure consistency in the prediction.