Several emerging wireless communication systems require direct transmission between mobile terminals to support efficient data transfer and user mobility. Such mobile-to-mobile communication systems differ from the conventional cellular systems where only the user unit is mobile. In addition, there might be a relay, also called a repeater, between the original transmitter and the final receiver to improve the network range and coverage. Potential applications for mobile-to-mobile systems include Intelligent Highways for coordinated traffic control and ad-hoc networks meant for military and disaster management. Relays may be deployed in cellular networks and IEEE 802.16 mesh networks for wireless broadband access. Extensive research in cellular radio channels has led to the successful deployment of cellular networks. However, our knowledge of the radio channels encountered in mobile-to-mobile and relay-based systems is still inadequate. This forms the primary motivation behind our research in addressing wireless channel modeling, simulation, and estimation issues for these systems. Specifically, we investigate frequency-flat mobile-to-mobile channels and develop simulation models by using the sum-of-sinusoids method, which is widely used for cellular channels. In addition, we present the properties of amplify and forward relay channels via theoretical analysis. This analysis, to the best of our knowledge, is the first of its kind. Further, we address the unique challenges, which arise because of the different underlying channel model, for channel estimation in amplify and forward relay systems. Our work would provide other researchers the necessary tools for the design and testing of these emerging communication systems.