This chapter notes that the use of cyberspace to carry out terrorist activities has continued to advance with the evolution of the internet and information technology. To date, there is no universally accepted definition of cyber-terrorism, which further explains why understanding of the term ‘cyber-terrorism’ is fairly limited; and in effect poses a bigger challenge as a fundamental issue and challenge in countering cyber-terrorism threats. The continuous misuse, misappropriation and the over-dramatization of the term cyber-terrorism has also shown that the apposite appreciation of the dangers attributable to cyber-terrorism must begin with a clear definition of it. As the growth of information technology continues in a geometric progression, computer systems and networks are daily scythed, leading to constant loss of critical information and data mostly because of the inability of law enforcement agencies to keep pace with the growth of connectivity, and hacking tools and techniques. Most of the critical infrastructures are always at risk because they are networked. This chapter seeks to answer questions like: what is cyber-terrorism and what are offences against critical infrastructure? Do these terms actually mean the same? The chapter explores the definitional aspects of cyber-terrorism and offences against the critical infrastructure and further, their disparate viewpoints, theoretical and actual forms. It is basically an analysis of the variety of the types of conducts that amount to cyber-terrorism in contradistinction to offences against the critical infrastructure, along with the adjectival law provisions. It x-rays the composition or elements of cyber-terrorism offences and procedural issues and challenges to the enforcement of cybercrime legislations, as applicable in Nigeria, while also making essential references to the relevant regional legislative enactments as might be applicable in the circumstance.