The benefits of the cyberspace are accompanied by the danger of cyber attacks. These vary in sophistication, and range in scale from attacks against individuals to attacks against countries, for example those on Estonia in April–May 2007. This paper will focus on the threat to what may be called primary Critical Information Infrastructure of Concern, and how to protect it. This topic will be set in the contexts of how cyberspace has spread globally, and Internet security. Secondly, we will consider the various threats to which cyberspace is exposed. It is the vehicle of, and the potential victim of, globalization. We will summarize the uses which terrorists have made of cyberspace. A range of measures are seen as essential for protecting critical infrastructure. Effective communication of R&D agendas will allow preventative steps to be taken, or attacks to be repelled as quickly as possible. Governments and the private sector should work to build cyber security capabilities, for example by forming CSIRTs. A legal framework for this new technology must be developed in terms of national legislation and, in view of the worldwide character of the networks, international conventions