Wireless power transfer (WPT) is a viable source of energy for wirelessly powered communication networks (WPCNs). In this paper, we first consider WPT from an energy access point (E-AP) to multiple energy receivers (E-Rs) to obtain the optimal policy that maximizes the WPT efficiency. For this purpose, we formulate the problem of maximizing the total average received power of the E-Rs subject to the average and peak power level constraints of the E-AP. The formulated problem is a non-convex stochastic optimization problem. Using some stochastic optimization techniques, we tackle the challenges of this problem and derive a closed-form expression for the optimal solution, which requires the explicit knowledge of the distribution of channel state information (CSI) in the network. We then propose a near-optimal algorithm that does not require any explicit knowledge of the CSI distribution and prove that the proposed algorithm attains a near-optimal solution within a guaranteed gap to the optimal solution. We next consider fairness among the E-Rs and propose a quality of service (QoS) aware fair policy that maximizes a generic network utility function while guaranteeing the required QoS of each E-R. Finally, we study a practical wirelessly powered communication scenario in which the E-Rs utilize their energy harvested through WPT to transmit information to the E-AP. We optimize the received information at the E-AP under its average and peak transmission power constraints and the fairness constraints of the E-Rs. Numerical results show the significant performance of our proposed solutions compared to the state-of-the-art baselines.