In this thesis we study three RWIRE models. A RWIRE is simply a random walk where the transition rates are themselves random variables. The first model studied is a unit jump non directed RWIRE in discrete and continuous time. Results are presented for the "speed" of the RWIRE in discrete time. It is also shown that the random environment slows down the random walk in the discrete time setting. The second model studied is a unit jump directed RWIRE in continuous time. Results for the "speed", the slow approach to infinity, and the limiting distribution are given for this model. It is also shown, as m the first model, that the random environment slows down the random walk. The final model is a multiple jump directed RWIRE in both discrete and continuous time The discrete model findings include the "speed" and the limiting distribution. For the continuous case the “speed" is derived.