Critical Infrastructures (CIs), such as healthcare facilities, power grids, transportation systems, and financial institutions, are vital components of a functioning society, with the economy and safety being dependent on them. Nevertheless, they have become increasingly vulnerable to cyber threats and attacks in recent years. The main reason is their inability to quickly adapt to technological changes, employ updated cryptographic frameworks, and implement a thoroughly secure architecture based on their characteristics. In this study, the unique complexities of these systems are highlighted. Various verified cyberattacks that were executed against CIs in recent years are analyzed. Moreover, the general framework of CIs is demonstrated together with the employed technologies and cryptographic primitives. A thorough architecture of said technologies is developed to better understand the targeted components and easily identify potentially hidden threats. Afterwards, threat, adversary, and attack models that target critical systems and services are designed. The purpose is a better comprehension of the systems’ vulnerabilities, attack structures, motives, and targets for assisting CIs’ designers in creating secure frameworks and mechanisms, with the ability to mitigate such threats. Lastly, security controls and cryptography frameworks are demonstrated together with efficient mitigation architectures and implementations from the research community.