In the recent years of advanced cyber attacks over the critical information infrastructure (CII) with a high cause of damage, including physical destruction, raised the fears that cyber terrorism is an imminent threat. Moreover, many experts and officials worldwide are trying to extend the term cyber terrorism to include hacktivism and terrorists' use of the cyberspace, which is causing a lot of confusion in defining what really cyber terrorism is. On the other hand, although different countries across the globe experience a different kind of cyber attacks on everyday basis, which also includes attacks against CII, up to now there is still not an example of a cyber attack that is officially recognized as an act of cyber terrorism. This chapter gives an overview of the possibilities offered to the terrorists by the cyberspace, mainly focusing on the explanation of the terms “terrorist use of cyberspace”, “cyber attacks”, and “cyber terrorism”. It argues that the cyberspace is more extensively used for support of different terrorists' activities as propaganda, radicalisation and recruitment, networking and secret communication, planning, command and control, funding training and data mining for potential targets to attack. Furthermore, it covers the aspect of cyber terrorism, as one of the future potential threats against the national and global security.