Quality of experience (QoE) is the perceptual quality of service (QoS) from the users' perspective. For video service, the relationship between QoE and QoS (such as coding parameters and network statistics) is complicated because users' perceptual video quality is subjective and diversified in different environments. Traditionally, QoE is obtained from subjective test, where human viewers evaluate the quality of tested videos under a laboratory environment. To avoid high cost and offline nature of such tests, objective quality models are developed to predict QoE based on objective QoS parameters, but it is still an indirect way to estimate QoE. With the rising popularity of video streaming over the Internet, data-driven QoE analysis models have newly emerged due to availability of large-scale data. In this paper, we give a comprehensive survey of the evolution of video quality assessment methods, analyzing their characteristics, advantages, and drawbacks. We also introduce QoE-based video applications and, finally, identify the future research directions of QoE.