High-precision indoor positioning is essential for various applications, such as the Internet of Things, robotics, and smart manufacturing, requiring accuracy better than 1 m. Conventional indoor positioning methods, like Wi-Fi or Bluetooth fingerprinting, typically provide low accuracy within a range of several meters, while techniques such as laser or visual odometry often require fusion with absolute positioning methods. Ultra-wideband (UWB) and Wi-Fi Round-Trip Time (RTT) are emerging radio positioning technologies supported by industry leaders like Apple and Google, respectively, both capable of achieving high-precision indoor positioning. This paper offers a comprehensive survey of UWB and Wi-Fi positioning, beginning with an overview of UWB and Wi-Fi RTT ranging, followed by an explanation of the fundamental principles of UWB and Wi-Fi RTT-based geometric positioning. Additionally, it compares the strengths and limitations of UWB and Wi-Fi RTT technologies and reviews advanced studies that address practical challenges in UWB and Wi-Fi RTT positioning, such as accuracy, reliability, continuity, and base station coordinate calibration issues. These challenges are primarily addressed through a multi-sensor fusion approach that integrates relative and absolute positioning. Finally, this paper highlights future directions for the development of UWB- and Wi-Fi RTT-based indoor positioning technologies.