Recognizing the various and broad range of applications of unmanned aerial vehicles (UAVs) and unmanned aircraft systems (UAS) for personal, public and military applications, recent un-intentional malfunctions of uncontrollable UAVs or intentional attacks on them divert our attention and motivate us to devise a protection system, referred to as a counter UAV system (CUS). The CUS, also known as a counter-drone system, protects personal, commercial, public, and military facilities and areas from uncontrollable and belligerent UAVs by neutralizing or destroying them. This paper provides a comprehensive survey of the CUS to describe the key technologies of the CUS and provide sufficient information with wich to comprehend this system. The first part starts with an introduction of general UAVs and the concept of the CUS. In the second part, we provide an extensive survey of the CUS through a top-down approach: i) the platform of CUS including ground and sky platforms and related networks; ii) the architecture of the CUS consisting of sensing systems, command-and-control (C2) systems, and mitigation systems; and iii) the devices and functions with the sensors for detection-and-identification and localization-and-tracking actions and mitigators for neutralization. The last part is devoted to a survey of the CUS market with relevant challenges and future visions. From the CUS market survey, potential readers can identify the major players in a CUS industry and obtain information with which to develop the CUS industry. A broad understanding gained from the survey overall will assist with the design of a holistic CUS and inspire cross-domain research across physical layer designs in wireless communications, CUS network designs, control theory, mechanics, and computer science, to enhance counter UAV techniques further.