Language involves several hierarchical levels of abstraction. Most models focus on a particular level of abstraction making them unable to model bottom-up and top-down processes. Moreover, we do not know how the brain grounds symbols to perceptions and how these symbols emerge throughout development. Experimental evidence suggests that perception and action shape one-another (e.g. motor areas activated during speech perception) but the precise mechanisms involved in this action-perception shaping at various levels of abstraction are still largely unknown. My previous and current work include the modelling of language comprehension, language acquisition with a robotic perspective, sensorimotor models and extended models of Reservoir Computing to model working memory and hierarchical processing. I propose to create a new generation of neural-based computational models of language processing and production; to use biologically plausible learning mechanisms relying on recurrent neural networks; create novel sensorimotor mechanisms to account for action-perception shaping; build hierarchical models from sensorimotor to sentence level; embody such models in robots.