This paper investigates the outage probability and the throughput of relay networks with wireless information and energy transfer where the relays harvest energy from the transmitted radio-frequency signal of the source. Considering different power consumption models, we derive the outage probability for both adaptive and non-adaptive power allocations at the relay. With a total energy consumption constraint at the source, we provide closed-form expressions for the optimal time sharing and power allocation between the source energy and information transfer signals as well as the optimal relay positioning such that the outage probability is minimized. Finally, we extend our analysis to multi-relay networks. We show that with perfect channel state information (CSI) available at the relays and $N$ relays the opportunistic relaying scheme achieves diversity order of $\frac{N+1}{2}$. Also, we analyze the opportunistic relaying with partial CSI where either the source-relay or the relay-destination CSI is provided at its corresponding transmit terminal, and prove that the relay selection based on the source-relay CSI outperforms the relay selection based on the relay-destination CSI, in terms of outage probability. The analytical and simulation results demonstrate the efficiency of wireless energy and information transfer systems in different conditions.