The advancement of technology indeed brings people close to one another through the use of the internet or network. It is indisputable, that the internet makes many parts of lives expedient, in terms of communication, health, education, and commercial activities. Cybercrime means a crime in which a computer was directly and significantly instrumental. A person who uses a computer to commit a crime is called a cybercriminal. Cyber terrorism is defined as any person, group, or organization who with terrorist intent, utilizes access, or aids in accessing a computer, electronic system, or electronic devices by any available means and thereby knowingly engages in or attempts to engage in terrorist acts and commit the offense of cyber terrorism. Hackers classified is into three classes; an unauthorized individual who intrudes into someone's computer is called a black hat hacker; an authorized individual working in an organization for detecting vulnerabilities to protect the network system is called a white hat hacker, and the hacker who shares the characteristics of black and white hat hackers is called grey hat hacker. There are numerous types of cybercrime or cyber-attack, this paper highlighted some common types of cyber-attacks which include; Denial of service attacks, Cyber-phishing, Cyber-stalking, Brute force attacks, etc.