The sense of embodiment refers to the sensations of being inside, having, and controlling a body. In virtual reality, it is possible to substitute a person's body with a virtual body, referred to as an avatar. Modulations of the sense of embodiment through modifications of this avatar have perceptual and behavioural consequences on users that can influence the way users interact with the virtual environment. Therefore, it is essential to define metrics that enable a reliable assessment of the sense of embodiment in virtual reality to better understand its dimensions, the way they interact, and their influence on the quality of interaction in the virtual environment. In this review, we first introduce the current knowledge on the sense of embodiment, its dimensions (senses of agency, body ownership, and self-location), and how they relate the ones with the others. Then, we dive into the different methods currently used to assess the sense of embodiment, ranging from questionnaires to neurophysiological measures. We provide a critical analysis of the existing metrics, discussing their advantages and drawbacks in the context of virtual reality. Notably, we argue that real-time measures of embodiment, which are also specific and do not require double tasking, are the most relevant in the context of virtual reality. Electroencephalography seems a good candidate for the future if its drawbacks (such as its sensitivity to movement and practicality) are improved. While the perfect metric has yet to be identified if it exists, this work provides clues on which metric to choose depending on the context, which should hopefully contribute to better assessing and understanding the sense of embodiment in virtual reality.