Network information theory explores the fundamental data transport limits over communication networks. Broadcasting and relaying are two natural models arising in communication contexts where multiple users share a common communication medium. Number of relay and broadcasting models are considered in this thesis. We first collect the existing methodologies of communication over a discrete memoryless relay channel. A new communication strategy over this channel is also proposed, which achieves the same data-rates as the best known schemes in literature, incurring a lower delay at the same time. We then consider the Gaussian broadcast channel (GBC), and show that its capacity region is enlarged by the availability of feedback, even if the feedback is from only one of the receivers. We further show a low complexity, explicit capacity achieving strategy over a GBC with degraded receivers. A combination of relay and broadcast models, called the relay-broadcast channel (RBC) is analyzed next. Achievable regions are proposed for different RBC scenarios. For the Gaussian version of an RBC, we characterize the complete capacity region when the receivers are degraded with respect to the relay. The final part of this thesis investigates communication over fading channels. We propose upper bounds for non-coherent, as well as lower bounds for coherent communication over a MIMO fading channel.