—We aim to characterize the maximum link throughput of a multi-channel opportunistic communication system. The states of these channels evolve as independent and identically distributed Markov processes (the Gilbert-Elliot channel model). A user, with limited sensing and access capability, chooses one channel to sense and access in each slot and collects a reward determined by the state of the chosen channel. Such a problem arises in cognitive radio networks for spectrum overlay, opportunistic transmissions in fading environments, and resource-constrained jamming and anti-jamming. The objective of this paper is to characterize the optimal performance of such systems. The problem can be generally formulated as obtaining the maximum expected long-term reward of a partially observable Markov decision process or a restless multi-armed bandit process, for which analytical characterizations are rare. Exploiting the structure and optimality of the myopic channel selection policy established...