Embodied cognition is a very broad term that covers many diverse approaches. They assume that the physical body of an agent is relevant to cognition, which essentially involves perception and action; in other words, cognition is not limited to the brain alone. This chapter starts from the proposal of Lawrence Shapiro to frame the significance of embodied cognition in terms of separate hypotheses. It characterizes embodied cognition, and the challenges inherent in understanding some non-trivial contribution of embodiment to the study of cognition. The chapter argues that embodied cognition is best understood as a complex research tradition, rather than a single theory or hypothesis. It examines challenges to computationalism as posed by theorists of embodiment to show that theories of embodied cognition have non-trivial assumptions. The chapter turns to embodiment and robotics, to discuss a computational approach to neuroethology and morphological computation. It concludes with a sketch of the place of embodied computation in cognitive science.