This report contains an overview of two related areas of research in cryptography which have been prolific in significant advances in recent years. The first of these areas is pairing based cryptography. Bilinear pairings over elliptic curves were initially used as formal mathematical tools and later as cryptanalysis tools that rendered supersingular curves insecure. In recent years, bilinear pairings have been used to construct many cryptographic schemes. The second area covered by this report is identity based cryptography. Digital certificates are a fundamental part of public key cryptography, as one needs a secure way of associating an agent’s identity with a random (meaningless) public key. In identity based cryptography, public keys can be arbitrary bit strings, including readable representations of one’s identity.