Grounded language acquisition is concerned with learning the meaning of language as it applies to the physical world. As robots become more capable and ubiquitous, there is an increasing need for non-specialists to interact with and control them, and natural language is an intuitive, flexible, and customizable mechanism for such communication. At the same time, physically embodied agents offer a way to learn to understand natural language in the context of the world to which it refers. This paper gives an overview of the research area, selected recent advances, and some future directions and challenges that remain.