Relay systems hold promise for next-generation wireless systems because such systems can satisfy users' demand for higher data rates, higher Quality-Of-Service (QOS), and provide enlarged service area with low cost and low complexity due to the simplicity of the function of a Relay Station (RS). Relay systems are naturally combined with Orthogonal Frequency Division Multiplexing (OFDM) based Frequency Division Multiple Access (OFDMA) systems because these systems efficiently mitigate multi-path fading and satisfy the users' demand by optimal rate- and power-allocation over subchannels. Therefore, OFDMA relay systems have received a lot of attention in recent years and much work has been published on the potential benefits of relay systems. However, to fully exploit the benefits of relaying, OFDMA relay systems require efficient management of resources including power, subchannels, and RS location because the actual data rate of multi-hop relaying is the minimum of the data rates of all hops. Thus, simply allocating more resources to any hop does not guarantee a higher overall data-rate. The difficulty of the resource-allocation is the non-convexity of the optimization problem caused by the interrelationship of all resources through RSs. Thus, many researchers have focused on a simplified system model with one RS and one user, which might be problematic in practical settings. This dissertation investigates the more generalized system model with unlimited number of RSs and users, and develops the optimal or near optimal resource-allocation algorithms for the generalized system model. Further, this dissertation shows the superiority of relay systems over current systems in terms of fairness and performance. The first part of the dissertation assumes that subchannels are preassigned to users or RSs to convert a sum-rate maximization problem into a convex problem, and to obtain intuition about how to allocate other resources, such as subchannels. The optimal power-allocation solution is a modification of the well known water-filling algorithm, which is efficiently solved with an inner-outer bisection method. By using the optimal power-allocation algorithm, the two-hop OFDMA relay systems outperform the conventional OFDMA systems by more than 25% ∼ 30%. Then, based on the optimality conditions of the power-allocation problem, the second part proposes three subchannel-allocation algorithms: an extended modified inverse subchannel signal-to-noise ratio algorithm, a bit accumulation algorithm, and a bit ratio algorithm. These algorithms are also based on the well-known data rate constraint: to maximize the data rate of multi-hop relaying, all the data rates of all hops should be equal. By using the proposed algorithms, the relay systems outperform current systems by 200% ∼ 370%, depending on the system power. This confirms that subchannel-allocation is a key factor in obtaining the significant performance gain promised by relay systems. To find the optimal RS location, this dissertation defines a relay gain, which is a metric that measures how much performance gain users are expected to obtain when they use relaying channels instead of direct channels. The relay gain originates from a virtual multi-user diversity gain and a virtual multi-path diversity gain. Because of the relay gain, the relay systems innately guarantee some amount of fairness. From the analysis of the relay gain, it is confirmed that the location of RSs controls the balance between performance and fairness and so relay systems should wisely choose RS locations to maximize both performance and fairness. Hence, based on the relay gain, the last part of the...