The Internet has made several giant leaps over the years, from a fixed to a mobile Internet, then to the Internet of Things, and now to a Tactile Internet. The Tactile Internet goes far beyond data, audio and video delivery over fixed and mobile networks, and even beyond allowing communication and collaboration among things. It is expected to enable haptic communications and allow skill set delivery over networks. Some examples of potential applications are tele-surgery, vehicle fleets, augmented reality and industrial process automation. Several papers already cover many of the Tactile Internet-related concepts and technologies, such as haptic codecs, applications, and supporting technologies. However, none of them offers a comprehensive survey of the Tactile Internet, including its architectures and algorithms. Furthermore, none of them provides a systematic and critical review of the existing solutions. To address these lacunae, we provide a comprehensive survey of the architectures and algorithms proposed to date for the Tactile Internet. In addition, we critically review them using a well-defined set of requirements and discuss some of the lessons learned as well as the most promising research directions.