This paper provides a comprehensive literature review on applications of economic and pricing theory to security issues in wireless networks. Unlike wireline networks, the broadcast nature and the highly dynamic change of network environments pose a number of nontrivial challenges to security design in wireless networks. While the security issues have not been completely solved by traditional or system-based solutions, economic and pricing models recently were employed as one efficient solution to discourage attackers and prevent attacks to be performed. In this paper, we review economic and pricing approaches proposed to address major security issues in wireless networks including eavesdropping attack, Denial-of-Service (DoS) attack such as jamming and Distributed DoS (DDoS), and illegitimate behaviors of malicious users. Additionally, we discuss integrating economic and pricing models with cryptography methods to reduce information privacy leakage as well as to guarantee the confidentiality and integrity of information in wireless networks. Finally, we highlight important challenges, open issues and future research directions of applying economic and pricing models to wireless security issues.