Grounded language acquisition is an important issue, particularly to facilitate human-robot interactions in an intelligent and effective way. The evolutionary and developmental language acquisition are two innovative and important methodologies for the grounding of language in cognitive agents or robots, the aim of which is to address current limitations in robot design. This paper concentrates on these two main modelling methods with the grounding principle for the acquisition of linguistic ability in cognitive agents or robots. This review not only presents a survey of the methodologies and relevant computational cognitive agents or robotic models, but also highlights the advantages and progress of these approaches for the language grounding issue.