Abstract Perceptual video quality assessment plays a vital role in the field of video processing due to the existence of quality degradations introduced in various stages of video signal acquisition, compression, transmission and display. With the advancement of Internet communication and cloud service technology, video content and traffic are growing exponentially, which further emphasizes the requirement for accurate and rapid assessment of video quality. Therefore, numerous subjective and objective video quality assessment studies have been conducted over the past two decades for both generic videos and specific videos such as streaming, user-generated content, 3D, virtual and augmented reality, high dynamic range, high frame rate, audio-visual, etc. This survey provides an up-to-date and comprehensive review of these video quality assessment studies. Specifically, we first review the subjective video quality assessment methodologies and databases, which are necessary for validating the performance of video quality metrics. Second, the objective video quality assessment measures for general purposes are categorized and surveyed according to the methodologies utilized in the quality measures. Third, we overview the objective video quality assessment measures for specific applications and emerging topics. Finally, the performance of the state-of-the-art video quality assessment measures is compared and analyzed. This survey provides a systematic overview of both classical works and recent progress in the realm of video quality assessment, which can help other researchers quickly access the field and conduct relevant research.