We consider optimal power allocation policies for a single server, multiuser wireless communication system. The transmission channel may experience multipath fading. We obtain very efficient, low computational complexity algorithms which minimize power and ensure stability of the data queues. We also obtain policies when the users may have mean delay constraints. If the power required is a linear function of rate then we exploit linearity and obtain linear programs with low complexity. We also provide closed-form optimal power policies when there is a hard deadline delay constraint. Later on, we also extend single hop results to multihop networks. First we consider the case, when the transmission rate is a linear function of power. We provide low complexity algorithms for joint routing, scheduling and power control which ensure stability of the queues, certain minimum rates, end-to-end hard deadlines, and/or upper bounds on the end-to-end mean delays. Further we extend these results to the multihop networks where the power is a general monotonically increasing function of rate. For our algorithms, we also provide rates of convergence to the stationary distributions for the queue length process and also approximate end-to-end mean delays. Finally, we provide computationally efficient algorithms that minimize the total power when there is a end-to-end hard deadline delay constraint.