Quality of experience (QoE) assessment for adaptive video streaming plays a significant role in advanced network management systems. It is especially challenging in case of dynamic adaptive streaming schemes over HTTP (DASH) which has increasingly complex characteristics including additional playback issues. In this paper, we provide a brief overview of adaptive video streaming quality assessment. Upon our review of related works, we analyze and compare different variations of objective QoE assessment models with or without using machine learning techniques for adaptive video streaming. Through the performance analysis, we observe that hybrid models perform better than both quality-of-service (QoS) driven QoE approaches and signal fidelity measurement. Moreover, the machine learning-based model slightly outperforms the model without using machine learning for the same setting. In addition, we find that existing video streaming QoE assessment models still have limited performance, which makes it difficult to be applied in practical communication systems. Therefore, based on the success of deep learned feature representations for traditional video quality prediction, we also apply the off-the-shelf deep convolutional neural network (DCNN) to evaluate the perceptual quality of streaming videos, where the spatio-temporal properties of streaming videos are taken into consideration. Experiments demonstrate its superiority, which sheds light on the future development of specifically designed deep learning frameworks for adaptive video streaming quality assessment. We believe this survey can serve as a guideline for QoE assessment of adaptive video streaming.