In today's Internet, video is the most dominant application and in addition to this, wireless networks such as WiFi, Cellular, and Bluetooth have become ubiquitous. Hence, most of the Internet traffic is video over wireless nodes. There is a plethora of research to improve video streaming to achieve high Quality of Experience (QoE) over the Internet. Many of them focus on wireless nodes. Recent measurement studies often show QoE of video suffers in many wireless clients over the Internet. Recently, many research papers have presented models and schemes to optimize the Adaptive BitRate (ABR) based video streaming for wireless and mobile users. In this survey, we present a comprehensive overview of recent work in the area of Internet video specially designed for wireless network. Recent research has suggested that there are some new challenges added by the connectivity of clients through wireless. Also these challenges become more difficult to handle when these nodes are mobile. This survey also discusses new potential areas of future research due to the increasing scarcity of wireless spectrum.