Elliptic Curve Cryptography (ECC) has emerged as a cornerstone of modern cryptographic protocols, offering robust security with smaller key sizes and improved efficiency compared to classical systems like RSA. By leveraging the mathematical properties of elliptic curves over finite fields, ECC enables secure key exchange, digital signatures, and encryption with reduced computational and bandwidth requirements. This article provides a comprehensive overview of ECC, the mathematical foundations underpinning its security, its key protocols—including ECDH, ECDSA, and ECIES—and its applications in contemporary digital security, from secure web communications to cryptocurrencies. The discussion also addresses practical considerations, implementation challenges, and the future trajectory of ECC in a post-quantum world.