Which is my body and how do I distinguish it from the bodies of others, or from objects in the surrounding environment? The perception of our own body and more particularly our sense of body ownership is taken for granted. Nevertheless, experimental findings from body ownership illusions (BOIs), show that under specific multisensory conditions, we can experience artificial body parts or fake bodies as our own body parts or body, respectively. The aim of the present paper is to discuss how and why BOIs are induced. We review several experimental findings concerning the spatial, temporal, and semantic principles of crossmodal stimuli that have been applied to induce BOIs. On the basis of these principles, we discuss theoretical approaches concerning the underlying mechanism of BOIs. We propose a conceptualization based on Bayesian causal inference for addressing how our nervous system could infer whether an object belongs to our own body, using multisensory, sensorimotor, and semantic information, and we discuss how this can account for several experimental findings. Finally, we point to neural network models as an implementational framework within which the computational problem behind BOIs could be addressed in the future.