To enhance the national security, there is a growing need for government agencies to legitimately monitor suspicious communication links for preventing intended crimes and terror attacks. In this paper, we propose a new wireless information surveillance paradigm by investigating a scenario where a legitimate monitor aims to intercept a suspicious wireless communication link over fading channels. The legitimate monitor can successfully eavesdrop (decode) the information of the suspicious link at each fading state only when its achievable data rate is no smaller than that at the suspicious receiver. In practice, such legitimate eavesdropping is particularly challenging, since the legitimate monitor may be far away from the suspicious transmitter and cannot eavesdrop efficiently. To overcome this issue, we propose a new approach, namely proactive eavesdropping via cognitive jamming, in which the legitimate monitor purposely jams the receiver so as to change the suspicious communication (e.g., to a smaller data rate) for overhearing more efficiently. In particular, we consider delay-sensitive and delay-tolerant applications for the suspicious data communications, under which the legitimate monitor maximizes the eavesdropping non-outage probability for event-based monitoring and the relative eavesdropping rate for content analysis, respectively, by optimizing its jamming power allocation over different fading states subject to an average power constraint. Numerical results show that the proposed proactive eavesdropping via cognitive jamming approach greatly outperforms the conventional passive eavesdropping without jamming and the proactive eavesdropping with constant-power jamming.