Energy harvesting (EH) is an innovative way to build long-term and self-sustainable wireless networks. However, an inconstant EH rate may have an adverse effect on the quality-of-service (QoS) of wireless traffic, such as packet delay and error. In this article we discuss techniques that provide QoS to EH powered wireless communications. A new "dynamic string tautening" method is presented to produce the most energy efficient schedule with substantially lower complexity, compared to convex optimization techniques. The method adapts to the bursty arrivals of wireless traffic and harvested energy, and ensures that delay-sensitive data will be delivered by deadline. Comprehensive designs of EH powered transmitters are also discussed, where the EH rate, battery capacity, and deadline requirement can be jointly adjusted to leverage QoS and the cost.