This paper studies the problem of secure communication over broadcast channels under the individual secrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant of each message (i.e., the information leakage from each message to the eavesdropper is made vanishing). Building upon Carleial-Hellman's secrecy coding, Wyner's secrecy coding, the frameworks of superposition coding and Marton's coding together with techniques such as rate splitting and indirect decoding, achievable rate regions are developed. The proposed regions are compared with those satisfying joint secrecy and without secrecy constraints, and the individual secrecy capacity regions for special cases are characterized. In particular, capacity region for the deterministic case is established, and for the Gaussian model, a constant gap (i.e., 0.5 bits within the individual secrecy capacity region) result is obtained. Overall, when compared with the joint secrecy constraint, the results allow for trading-off secrecy level and throughput in the system.