The forthcoming generation of wireless technology, 6G, aims to usher in an era of ubiquitous intelligent services, where everything is interconnected and intelligent. This vision requires the seamless integration of three fundamental modules: Sensing for information acquisition, communication for information sharing, and computation for information processing and decision-making. These modules are intricately linked, especially in complex tasks such as edge learning and inference. However, the performance of these modules is interdependent, creating a resource competition for time, energy, and bandwidth. Existing techniques like integrated communication and computation (ICC), integrated sensing and computation (ISC), and integrated sensing and communication (ISAC) have made partial strides in addressing this challenge, but they fall short of meeting the extreme performance requirements. To overcome these limitations, it is essential to develop new techniques that comprehensively integrate sensing, communication, and computation. This integrated approach, known as Integrated Sensing, Communication, and Computation (ISCC), offers a systematic perspective for enhancing task performance. This paper begins with a comprehensive survey of historic and related techniques such as ICC, ISC, and ISAC, highlighting their strengths and limitations. It then discusses the benefits, functions, and challenges of ISCC. Subsequently, the state-of-the-art signal designs for ISCC, along with network resource management strategies specifically tailored for ISCC are explored. Furthermore, this paper discusses the exciting research opportunities that lie ahead for implementing ISCC in future advanced networks, and the unresolved issues requiring further investigation. ISCC is expected to unlock the full potential of intelligent connectivity, paving the way for groundbreaking applications and services.