As demands on the network continue to grow, it is increasingly important to upgrade the existing infrastructure in order to offer higher bandwidth and service level guarantees to users. Next generation networks (NGNs) represent a fully IP-based architecture that is able to support different technologies. In this context, the satellite networks are considered a fundamental part for future hybrid architectures. In this scenario, knowing satellite channel propagation characteristics in order to be able to design a communication system to respond to new user needs is of fundamental importance. Many papers in the literature show channel models in different satellite scenarios both for fixed and mobile applications; however, to the best of our knowledge, nobody presents an overview on different satellite models based on Markov chains. This paper wants to present a comprehensive review of the most recent developments in satellite channel communications related to mobile services and, in particular, for the land mobile satellite systems. The work presents all different types of Markov models, from single-state to multi-state models, that have been proposed in the literature from the early 1980s.