We consider the so called “wire-tap channel”, where a transmitter sends secret information to its receiver in the presence of an eavesdropping receiver with similar signal processing capability as the desired receiver. It is assumed that all the communication links have time varying signal strengths which are only known at the corresponding receivers and not at the transmitter. In this thesis, we address the problem of characterizing the maximum possible rate of secret and reliable information transmission on such a wire-tap channel. We first characterize the secrecy capacity of a corresponding layered abstraction of the channel, and then, we derive an upper bound to the secrecy capacity of the fading wire-tap channel. Finally, we show that the wireless channels in the urban and most of the rural environments belong to a class of channels called Stochastically degraded channels, for which we have characterized the exact capacity in this thesis work.