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The material in this paper was presented in part at the 4th IEEE Workshop on Cooperative and Cognitive Mobile Networks (CoCoNet), collocated with IEEE ICC 2012. This paper investigates cooperation for secrecy in cognitive radio networks. In particular, we consider a four-node cognitive scenario where the secondary receiver is treated as a potential eavesdropper with respect to the primary transmission. The cognitive transmitter can help the primary transmission, and it should also ensure that the primary message is not leaked to the secondary user. We consider two cognitive scenarios depending on whether the secondary transmitter knows the primary message or not. In the first case, the secondary transmitter is unaware of the primary transmitter's message and acts as a helping interferer to enhance the secrecy of the primary transmission, whereas in the second case, relaying of the primary message is also within its capabilities. First, we find achievable rate regions for these two scenarios in the case of AWGN channels. We then investigate three different optimization problems: the maximization of the primary rate, the maximization of the secondary rate and the minimization of the secondary transmit power. For these optimization problems, we find closed-form expressions in important special cases. Furthermore, we analyze the cooperation between the primary and secondary transmitters from a game-theoretic perspective. We model their interaction as a Stackelberg game, for which we define and find the Stackelberg equilibrium. Finally, we use numerical examples to illustrate the rate regions, the three optimizations, and the impact of the Stackelberg game on the achievable rates and on the transmission strategies of the secondary transmitter. Refereed/Peer-reviewed