Grounded theories assume that there is no central module for cognition. According to this view, all cognitive phenomena, including those considered the province of amodal cognition such as reasoning, numeric, and language processing, are ultimately grounded in (and emerge from) a variety of bodily, affective, perceptual, and motor processes. The development and expression of cognition is constrained by the embodiment of cognitive agents and various contextual factors (physical and social) in which they are immersed. The grounded framework has received numerous empirical confirmations. Still, there are very few explicit computational models that implement grounding in sensory, motor and affective processes as intrinsic to cognition, and demonstrate that grounded theories can mechanistically implement higher cognitive abilities. We propose a new alliance between grounded cognition and computational modeling toward a novel multidisciplinary enterprise: Computational Grounded Cognition. We clarify the defining features of this novel approach and emphasize the importance of using the methodology of Cognitive Robotics, which permits simultaneous consideration of multiple aspects of grounding, embodiment, and situatedness, showing how they constrain the development and expression of cognition.