We survey the state of research on identity-based cryptography and attribute-based cryptography. We firstly review the basic concepts of identity-based cryptographic schemes in which users’ identifier information such as email or IP addresses instead of digital certificates can be used as public key for encryption or signature verification, and subsequently review some important identity-based encryption,signature and signcryption schemes. Then we give our research on Identity-Based Encryption-Signature (IBES) method. We also survey the attribute-based cryptographic schemes in which the identity of user is viewed as a set of descriptive attributes, including some important attribute-based encryption and signature schemes. We subsequently give our research on Attribute-Based Encryption and Identity-Based Signature (ABE-IBS) method. Both methods aim at efficiently improving the security of wireless sensor network. Finally,we propose a few interesting open problems concing with practical and theoretical aspects of identity-based cryptography and attribute-based cryptography.