State-dependent broadcast channels (BC) with heterogeneous channel state information available at the transmitter (CSIT) are studied. The heterogeneity of CSIT lies in the timeliness of channel state that governs the link from the transmitter to different receivers - CSI of each link can be perfectly (causally or non-causally), delayed, or not available at the transmitter. We focus on the erasure BC and the bursty Gaussian BC, where the channel states are governed by memoryless Bernoulli processes, independent across users. For the erasure BC with perfect single-user CSIT, we characterize its capacity region regardless of the CSIT of the other user and show that this capacity region strictly contains that with no CSIT. For the case with delayed single-user CSIT, we propose an opportunistic network coding scheme that achieves a strictly larger rate region than the no-CSIT capacity region. These results are extended to the bursty Gaussian BC, where for the perfect single-user CSIT scenario, the capacity region is characterized to within a bounded gap; and for the delayed single-user CSIT scenario, a rate region based the opportunistic network coding scheme is derived. As a corollary, single-user CSIT is able to increase the sum degrees of freedom (DoF) for bursty Gaussian BC. Our result is in sharp contrast to the recent negative result by Davoodi and Jafar , where it is shown that for fast-fading MISO broadcast channel, single-user CSIT does not help at all in terms of sum DoF.