With the rapid development of Radio Frequency Identification (RFID) technology, security and privacy in RFID systems have become critical issues for many applications. Due to the tight cost and extremely constrained resources of passive RFID tags, traditional cryptographic primitives designed for full-fledged computers might not be suited for securing RFID systems. There is a need of lightweight cryptographic primitives that can perform strong authentication and encryption, and provide other security functionalities for low-cost RFID tags. During the past few years, a multitude of lightweight cryptographic primitives such as lightweight block ciphers, stream ciphers, and pseudorandom number generators (PRNGs) have been designed for providing confidentiality and authenticity for passive RFID tags. In this chapter, we provide a research survey on recently proposed lightweight cryptographic primitives. For each cipher design we provide an overview of the description about the design, implementation, and existing attacks. Moreover, we also conduct an extensive comparison among different primitives in term of their design and performance.