The capacity regions are investigated for cooperative relay broadcast channels (RBCs), where relay links are incorporated into standard two-user broadcast channels to support user cooperation. The Partially Cooperative Relay Broadcast Channel is first studied, where only one user is allowed to transmit to the other user through a relay link. An upper bound on the capacity region is derived and is shown to be tighter than the cut-set bound. Two Gaussian cases are studied. The capacity region is established for the D-AWGN Partially Cooperative RBC, where the Gaussian noise terms at the two receivers are physically degraded. An upper bound on the capacity region is provided for the AWGN Partially Cooperative RBC, where the Gaussian noise terms at two receivers are independent, and this upper bound is shown to be close to the previously known lower bound. Furthermore, the capacity region for the Partially Cooperative RBC with feedback is established, and it is shown that feedback does not increase the capacity region for the degraded Partially Cooperative RBC. The Fully Cooperative RBC is further investigated, which is a more general class of cooperative relay broadcast channels with both users being allowed to transmit information to each other through relay links. All the results for Partially Cooperative RBCs are correspondingly generalized to Fully Cooperative RBCs. In particular, the capacity regions are established for the degraded Fully Cooperative RBC and its Gaussian example, and for the Fully Cooperative RBC with feedback. It is also shown that the AWGN Fully Cooperative RBC has a larger achievable rate region than the AWGN Partially Cooperative RBC.