This chapter explores the growing field of secure multi-party computation (SMPC), an important part of modern cryptography that protects privacy in group computing tasks. It does this by looking at their architectural designs, security models, ways to make them more efficient, and cross-domain uses. It goes into detail about the complex architecture and cryptographic methods that support SMPC, such as homomorphic encryption and sharing secrets, which protect the privacy and integrity of data in computations involving more than one person. This part also talks about strong security models that can protect against a wide range of threats, as well as ways to make algorithmic design and protocol implementation more efficient. In addition, it talks about how SMPC can be used in many different areas, like healthcare, banking, and AI, and stresses the need to follow privacy rules like GDPR. The chapter ends with a look ahead, talking about new challenges and trends that are coming up.