We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural results on the optimal scheduling policy using dynamic programming and assuming that the channel statistics is known. We prove that the Q-factor is monotonic and submodular, which leads to threshold-like structures in both problems. Then we develop a stochastic approximation and parameter learning frameworks to deal with the two scheduling problems with unknown channel statistics. We utilize their structures to design specialized learning algorithms. We prove the convergence of these algorithms. Performance improvement compared with the standard Q-learning algorithm is shown through numerical examples, which also discuss an alternative method based on recursive estimation of the channel quality.