In this paper, the authors survey the state of research on Identity-Based cryptography (IBC) and compare it with the traditional public key encryption. IBC is an emerging area of public key cryptography. They first reviewing the basic concepts of IBE and Identity Based Signature (IBS) schemes, and subsequently review some important IBE schemes based on the bilinear pairing, a computational primitive widely used to build up various identity-based cryptographic schemes in the current literature. They compare IBE with the traditional public key encryption. Finally, they discuss advantages and disadvantages of IBC with applications of IBC.