In this paper, we investigate the performance of dual‐hop relaying networks with wireless energy harvesting at the relay node over generalized η‐μ and κ‐μ fading channels. Our analysis considers decode‐and‐forward relays with a single antenna as well as source and destination nodes equipped with a single antenna. Specifically, we derive an accurate approximate analytical expression for the system outage probability (OP). The derived OP considers 3 different energy harvesting mechanisms: (1) time switching–based relaying, (2) power splitting–based relaying, and (3) ideal relaying receiver. Furthermore, we obtain accurate approximate analytical expressions for the system ergodic capacity and achievable throughput for the time switching–based relaying, power splitting–based relaying, and ideal relaying receiver. In addition, an accurate approximate analytical expression for the average bit error rate for several coherent modulation schemes is obtained. Through some numerical examples, we study the OP, throughput, and average bit‐error‐rate performance of the overall system under different system parameters such as fading parameters, energy harvesting time, power splitting factor, and signal‐to‐noise ratio. The results show that the effect of increasing the fading parameter μ on the system performance is more pronounced than that of increasing the fading parameters η and κ. Besides, increasing the energy harvesting time or the power splitting factor may be either beneficial or harmful for the throughput performance. Our numerical results are accompanied with Monte Carlo simulations to verify the accuracy of our analysis.