Results on physical-layer security and cooperative relaying are presented. In the physical layer security, the fading broadcast channel is first studied, where a source node transmits to two users over fading channels. The source node has common information for both users, and has confidential information only for one user and wishes to keep confidential information secret from the other user. Secrecy capacity region and the optimal resource allocations that achieve the boundary of the secrecy capacity region are established. The multiple access channel with confidential messages is then studied, where both users want to transmit their confidential information to one destination node and wish to keep their own information secret from the other user (eavesdropper). Secrecy capacity region is established for the case with one confidential message set. Secrecy capacity regions are also established for the Gaussian and binary channel examples. An achievable secrecy rate region is obtained for the case with two confidential message sets. In the cooperative relaying, relay broadcast channels (RBCs) are investigated, which model broadcast channels with receivers cooperating via relay communication. Inner and outer bounds on the capacity regions of these RBCs are obtained. Capacity regions are established for some classes of channels. New bounds on the broadcast channel are also established.