While cloud servers provide a tremendous amount of resources for networked video applications, most successful stories of cloud-assisted video applications are presentational video services, such as YouTube and NetFlix. This article surveys the recent advances on delay-sensitive video computations in the cloud, which are crucial to cloud-assisted conversational video services, such as cloud gaming, Virtual Reality (VR), Augmented Reality (AR), and telepresence. Supporting conversational video services with cloud resources is challenging because most cloud servers are far away from the end users while these services incur the following stringent requirements: high bandwidth, short delay, and high heterogeneity. In this article, we cover the literature with a top-down approach: from applications and experience, to architecture and management, and to optimization in and outside of the cloud. We also point out major open challenges, hoping to stimulate more research activities in this emerging and exciting direction.