Cyber-attacks have become a significant threat to national and international critical infrastructures (CIs), posing severe risks to national and global security, economic stability, and public safety. These attacks have been targeting various sectors, including communication, energy, health, transportation, and finance, all vital to the functioning of our societies. Recent years have seen the increased involvement of organized crime groups (OCGs) and organized cybercrime groups (OCCGs) in both state-sponsored and non-state-sponsored attacks against CIs, an issue deserving the attention of security scholars, experts, and policymakers. This chapter examines the involvement of OCGs and OCCGS in state-sponsored and non-state-sponsored cyber-attacks against CIs. The examination delves into their motivations, modus operandi, effects, and available measures to respond, focusing particularly on the European Union (EU) as a regional organization. By furthering our understanding of the complex dynamics between OCGs, state entities, and national security, scholars and practitioners will be able to identify weaknesses in strategies for deterring and managing threats caused by illicit organizations.