Cyber-attacks have become as commonplace as the Internet itself. Each year, industry reports, media outlets and academic articles highlight this increased prevalence, spanning both the amount and variety of attacks and cybercrimes. In this article, we seek to further advance discussions on cyber threats, cognitive vulnerabilities and cyberpsychology through a critical reflection on the social and psychological aspects related to cyber-attacks. In particular, we are interested in understanding how members of the public perceive and engage with risk and how they are impacted during and after a cyber-attack has occurred. This research focuses on key cognitive issues relevant to comprehending public reactions to malicious cyber events including risk perception, protection motivation, culture, and attacker characteristics (e.g., attacker identity, target identity and scale of attack). To consider the applicability of our findings, we investigate two significant cyber-attacks over the last few years, namely the WannaCry attack of 2017 and the Lloyds Banking Group attack in the same year.