Video content is quickly dominating the traffic over wireless networks and is creating significant challenges for managing this traffic efficiently while still delivering an acceptable quality of experience (QoE) to the end user. HTTP-based adaptive streaming techniques are growing in popularity to deliver video content from over-the-top providers to mobile devices, but have not yet been specifically optimized for wireless networks. This paper will present the latest activities on optimizing adaptive streaming protocols for LTE-Advanced wireless networks, including simulation results highlighting the factors which impact the QoE for video streaming applications in mobile networks, new QoE subjective tests and objective predictions which can be used for improving the efficiency of streaming, and capacity analysis with client-based feedback mechanisms to enable a more coordinated and optimized end-to-end system.