Identity-based cryptography is a new development of public-key cryptography. It was first proposed by Adi Shamir at CRYPTO'84. However, it took the cryptographic community a long while to produce effective identity-based cryptosystems. Indeed, this solution only appeared at the beginning of the twenty-first century. Nowadays, identity-based cryptography has become a very active field of research. This introductory chapter presents the basics of identity-based cryptography and briefly surveys its early history.