In the Reliable Broadcast Problem, a processor disseminates a value to all other processors in a distributed system where both processors and communication components are subject to failures. Solutions to this Reliable Broadcast problem are at the heart of most fault-tolerant applications. We characterize the execution of Reliable Broadcast protocols as a function of the properties of the underlying communication network. The class of networks considered includes familiar communication structures constructed out of fully-connected point-to-point graphs, linear chains, rings, broadcast networks (such as Ethernet) and buses. We derive a protocol that implements Reliable Broadcast for any member within this class. The execution time of the protocol is a linear function of the two parameters that characterize each network instance. The hardware-software tradeoffs that are revealed between performance, resiliency and network cost offer many new alternatives previously not considered in designing fault-tolerant systems.