The computational modeling of emotion has been an area of growing interest in cognitive robotics research in recent years, but also a source of contention regarding how to conceive of emotion and how to model it. In this paper, emotion is characterized as (a) closely connected to embodied cognition, (b) grounded in homeostatic bodily regulation, and (c) a powerful organizational principle—affective modulation of behavioral and cognitive mechanisms—that is ‘useful’ in both biological brains and robotic cognitive architectures. We elaborate how emotion theories and models centered on core neurological structures in the mammalian brain, and inspired by embodied, dynamical, and enactive approaches in cognitive science, may impact on computational and robotic modeling. In light of the theoretical discussion, work in progress on the development of an embodied cognitive-affective architecture for robots is presented, incorporating aspects of the theories discussed.