The growing consumer demand for mobile video services is one of the key drivers of the evolution of new wireless multimedia solutions requiring exploration of new ways to optimize future wireless networks for video services towards delivering enhanced quality of experience (QoE). One of these key video enhancing solutions is HTTP adaptive streaming (HAS), which has recently been spreading as a form of Internet video delivery and is expected to be deployed more broadly over the next few years. As a relatively new technology in comparison with traditional push-based adaptive streaming techniques, deployment of HAS presents new challenges and opportunities for content developers, service providers, network operators and device manufacturers. One of these important challenges is developing evaluation methodologies and performance metrics to accurately assess user QoE for HAS services, and effectively utilizing these metrics for service provisioning and optimizing network adaptation. In that vein, this article provides an overview of HAS concepts, and reviews the recently standardized QoE metrics and reporting framework in 3GPP. Furthermore, we present an end-to-end QoE evaluation study on HAS conducted over 3GPP LTE networks and conclude with a discussion of future challenges and opportunities in QoE optimization for HAS services.