In this thesis, we study the downlink multiuser scheduling and power allocation problem for systems with simultaneous wireless information and power transfer (SWIPT). In the first part of the thesis, we focus on multiuser scheduling. We design optimal scheduling algorithms that maximize the long-term average system throughput under different fairness requirements, such as proportional fairness and equal throughput fairness. In particular, the algorithm designs are formulated as non-convex optimization problems which take into account the minimum required average sum harvested energy in the system. The problems are solved by using convex optimization techniques and the proposed optimization framework reveals the tradeoff between the long-term average system throughput and the sum harvested energy in multiuser systems with fairness constraints. Simulation results demonstrate that substantial performance gains can be achieved by the proposed optimization framework compared to existing suboptimal scheduling algorithms from the literature. In the second part of the thesis, we investigate the joint user scheduling and power allocation algorithm design for SWIPT systems. The algorithm design is formulated as a non-convex optimization problem which maximizes the achievable rate subject to a minimum required average power transfer. Subsequently, the non-convex optimization problem is reformulated by big-M method which can be solved optimally. Furthermore, we show that joint power allocation and user scheduling is an efficient way to enlarge the feasible trade-off region for improving the system performance in terms of achievable data rate and harvested energy.