This special issue includes research articles which apply spoken language processing to robots that interact with human users through speech, possibly combined with other modalities. Robots that can listen to human speech, understand it, interact according to the conveyed meaning, and respond represent major research and technological challenges. Their common aim is to equip robots with natural interaction abilities. However, robotics and spoken language processing are areas that are typically studied within their respective communities with limited communication across disciplinary boundaries. The articles in this special issue represent examples that address the need for an increased multidisciplinary exchange of ideas.