Due to the rapidly increasing number of devices in wireless networks with the proliferation of applications based on new technologies such as machine to machine communications and Internet of Things, there is a growing interest in the random access schemes as they provide a simple means of channel access. To this end, various schemes have been proposed based on the ALOHA protocol to increase the e ciency of the medium access control layer over the last decade. On the other hand, physical layer aspects of random access networks have received relatively limited attention, and there is a need to consider optimal use of the underlying physical layer properties especially for transmission over wireless channels. In this thesis, we study uncoordinated random access schemes over wireless fading channels where each user independently decides whether to send a packet or not to a common receiver at any given time slot. To characterize the system throughput, i.e., the expected sum-rate, an information theoretic formulation is developed. We consider two scenarios: classical slotted ALOHA, where no multiuser detection (MUD) capability is available and slotted ALOHA with MUD. Our main contribution is that the optimal rates and the channel activity probabilities can be characterized as a function of the user distances to the receiver to maximize the system throughput in each case (more precisely, as a function of the average signal to noise ratios of the users). We use Rayleigh fading as our main channel model, however, we also study the cases where log-normal shadowing is observed along with small scale fading. Our proposed optimal rate selection schemes o er signi cant increase in expected system throughput compared to the same rate approach commonly used in the literature. In addition to the overall throughput optimization, the issue of fairness among users is also investigated and solutions which guarantee a minimum amount of individual throughput are developed. We also design systems with limited individual outage probabilities of the users for increased energy e ciency and reduced delay. All of these analytical works are supported with detailed numerical examples, and the performance of the proposed methods are evaluated.