Fault injection attacks are a powerful technique that intentionally induces faults during computations to leak secret information. This thesis studies the fault injection attack techniques. The thesis first categorizes various fault attack methods by fault model and fault analysis and gives examples of the various fault attacks on symmetric key cryptosystems and public key cryptosystems. The thesis then demonstrates fault injection attacks on RSA-CRT and constant time CSIDH. The fault attack consists of two main components: fault modeling, which examines methods for injecting faults in a target device, and fault analysis, which analyzes the resulting faulty outputs to deduce secrets in each cryptosystem. The thesis aims to provide a comprehensive survey on fault attack research, directions for further study on securing real-world cryptosystems against fault injection attacks, testing fault injection attacks with RSA-CRT, and demonstrate and evaluate fault injection attacks on constant time CSIDH. / Master of Science / Fault injection attacks are attacks where the attackers intentionally induce the fault in the device during the operation to obtain or recover secret information. The induced fault will impact the operation and cause the faulty output, providing the information to attackers. Many cryptographic algorithms and devices have been proven vulnerable to fault injection attacks. Cryptography is essential nowadays, as it is used to secure and protect confidential data. If the cryptosystem is broken, many system today will be compromised. Thus, this thesis focus on the fault injection attacks on the cryptosystems. This thesis introduces the background of fault injection attacks, categorizes them into different types, and provides examples of the attacks on cryptosystems. The thesis studies how the attacks work, including how the attack induces the fault in the device and how the attack analyzes the fault output they obtained. Specifically, I examine how these attacks affect two commonly used encryption methods: symmetric key cryptography and public key cryptography. Additionally, I implement the fault injection attack on RSA-CRT and emph{Commutative Supersingular Isogeny Diffie-Hellman}~(CSIDH). This research aims to understand the potential attack method on different cryptosystems and can explore mitigation or protection in the future.