A revolutionary effort to seek fundamental improvement of 802.11, known as IEEE 802.11ax, has been approved to deliver the next-generation wireless local area network (WLAN) technologies. In WLANs, medium access control protocol is the key component that enables efficient sharing the common radio channel while satisfying the quality of service (QoS) requirements for multimedia applications. With the new physical layer design and subsequent new medium access control functions under more demands on QoS and user experience, in this paper, we first survey the QoS support in legacy 802.11. Then, we summarize the IEEE 802.11ax standardization activities in progress and present an overview of current perspectives and expected features on medium access control protocol design to better support QoS and user experience in 802.11ax. We present the motivation behind, explain design principles, and identify new research challenges. To better satisfy customer needs on high bandwidth and low latency, emerging long-term evolution licensed-assisted access and its impacts to QoS provisioning in IEEE 802.11ax are further addressed given the collaboration between cellular and WLANs, and given the trend of 5G cellular over unlicensed bands.