Key Management in symmetric cryptography is to securely share a secret key between the two communicating individuals. The popular solution to this key management issue is to use public key cryptography schemes. The key management techniques are broadly classified into Key Distribution protocols and Key Agreement protocols. This paper presents the detailed classification of Key Agreement protocols and provides some of the existing ECC based protocols in each category. Recently much work has been carried out in Identity Based Cryptography IBC, Certificateless Public Key Cryptography CLPKC and Pairing Based Cryptography PBC based techniques for key agreement. This paper also presents the comparison of two-party key agreement protocols under these areas based on the computational cost calculated in the key agreement phase.