The full connectivity offered by the nature of wireless communication poses a vast number of benefits and challenges to the designers of future generation wireless networks. One of the main challenges being faced is dealing with the unresolvable interference at the receivers. It is widely recognized that the heart of this challenge lies in the design of resource allocation schemes which provide the best trade-off between efficiency and complexity Exploration of this trade-off requires appropriate choices of performance metrics and mathematical models. In this regard, the thesis is concerned with certain technical and mathematical aspects of resource allocation in wireless networks. We specifically argue that an efficient resource allocation in wireless networks needs to take into account the following parameters: (i) rate of environment changes, (ii) traffic model, and (iii) amount of information available at transmitters. As mathematical tools for our investigation, we use optimization theory and game theory. We are especially interested in distributed resource allocation in networks with slow fading channels and with partial channel side information at the transmitters. Transmitters with partial channel side information have exact information of their own channel as well as statistical knowledge of other channels. In such a context, the system is inherently impaired by a nonzero outage probability. We propose low complexity distributed algorithms for joint rate and power allocation, aiming at maximizing the individual throughput, defined as the successfully-received-information rate, under a power constraint.