Education is one of the essential foundations of the sustainable development of societies, in particular, the objectives SDG4 of the UN General Assembly. Extended Reality (XR, so-called Metaverse) enables multisensory interaction with virtual environments, computer-created objects, and avatars. Also, the dynamic development of Head Mounted Displays (HDMs) allows for an increasingly deeper experience of the virtual world, especially through the development of depth perception, including the rendering of several modalities like vision, touch, and hearing. This creates a unique opportunity to revolutionize the higher education system by adding a new dimension of cognition and making it accessible to more people, especially those living in hard-to-reach areas. It is also a perfect complement to the process of educating students during a pandemic, such as the recent COVID-19 pandemic. In this paper, based on the literature and our experience, we provided an overview of the possibility of the Metaverse application in higher education taking into account the advantages and limitations of the systems. It turned out that XR-based solutions can be successfully applied in medical education, chemistry courses as well as in Science, Technology, Engineering, and Mathematics (STEM) education. Moreover, the XR-based systems are useful for learning spatial skills such as navigation, spatial reasoning, and perception. In the case of remote learning, XR enables easier adaptation to the educational formula. Also, during lockdowns, an XR-based application can be considered a tool to promote socialization in the event. Thus, it enables to implementation of open and inclusive learning and teaching space, namely Edu-Metaverse. In the current social context, the obtained results provided valuable insights into factors affecting the users during the application of Metaverse in education processes, including remote learning. Finally, this paper suggests a research direction for the development of effective Metaverse-based educational solutions.