Research on embodiment of objects external to the human body has revealed important information about how the human nervous system interacts with robotic lower limb exoskeletons. Typical robotic exoskeleton control approaches view the controllers as an external agent intending to move in coordination with the human. However, principles of embodiment suggest that the exoskeleton controller should ideally coordinate with the human such that the nervous system can adequately model the input-output dynamics of the exoskeleton controller. Measuring embodiment of exoskeletons should be a necessary step in the exoskeleton development and prototyping process. Researchers need to establish high fidelity quantitative measures of embodiment, rather than relying on current qualitative survey measures. Mobile brain imaging techniques, such as high-density electroencephalography, is likely to provide a deeper understanding of embodiment during human-machine interactions and advance exoskeleton research and development. In this review we show why future exoskeleton research should include quantitative measures of embodiment as a metric of success.