In this dissertation we investigate resource allocation in fading channels with delay constraints. We first consider scheduling communication resources over time-varying channels when constrained by a hard deadline requirement. The basic problem setting is given as follows: a packet of B bits must be transmitted by a hard deadline of T time slots over a time-varying channel. The transmitter/scheduler must determine how many bits to transmit, or equivalently how much energy to transmit with, during each time slot based on the current channel quality and the number of unserved bits, with the objective of minimizing expected total energy. Our focus is on the interplay between opportunism (adapting to the fading behavior) and the delay requirements. Under the Shannon energy cost function, the optimal solution can only be numerically determined in general, and thus we develop simple and near-optimal policies, which are shown to be asymptotically optimal. Then, we consider monomial cost, under which we can obtain the optimal policy in closed form. We attempt to extend the result to the case for multi-user scheduling and scheduling with outage. In these resource allocation problems, our interests are in formulating an analytical solution. Additionally, we consider parallel/MIMO channel scheduling and wideband scheduling with a hard deadline constraint. As an alternative view of delay requirements, we consider the fairness of each user's traffic. In this regard, we investigate the symmetric capacity of MIMO broadcast channels along with high SNR analysis of MIMO broadcast channels.