Elliptic curves are some specific type of curves known as hyper elliptic curves. Compared to the integer factorization problem(IFP) based systems, using elliptic curve based cryptography will significantly decrease key size of the encryption. Therefore, application of this type of cryptography in systems that need high security and smaller key size has found great attention. Hyperelliptic curves help to make key length shorter. Many investigations are done with regard to improving computations, hardware and software implementation of these curves, their security and resistance against attacks. This paper studies and analyzes researches done about security and efficiency of hyperelliptic curves.