Isomorphism and homomorphism are fundamental concepts in mathematics and computer science, each playing crucial roles in various theoretical frameworks and practical applications. Isomorphism refers to a objective homomorphism that preserves structure, often used to establish equivalences between mathematical objects or structures. Homomorphism, on the other hand, preserves operations and relations between objects, enabling transformations and mappings within algebraic systems. In real-world implementations, these concepts find applications across diverse fields such as cryptography, graph theory, and database management. Isomorphism facilitates the equivalence of cryptographic keys and structures, ensuring secure communication channels. Homomorphism enables operations on encrypted data without decryption, crucial in privacy-preserving computations and secure multiparty computation protocols. This paper reviews the theoretical underpinnings of isomorphism and homomorphism, exploring their roles in various domains. It examines their practical implementations, highlighting their impact on enhancing security, efficiency, and computational capabilities in modern systems. Through examples and case studies, the paper illustrates how these concepts contribute to advancing technological solutions, emphasizing their importance in contemporary mathematics and computing.