Elliptic curve cryptography or ECC is a public-key cryptosystem. This paper introduces ECC and describes its present applications. A mathematical background is given initially. Then its’ major cryptographic uses are given. These include its’ use in encryption, key sharing and digital signatures. The security of these ECC-based cryptosystems are discussed. It was found that ECC was well suited for low-power and resource constrained devices because of its’ small key size.