Carbon fiber reinforced polymer (CFRP) tendons are composite materials that offer significant advantages in terms of tensile strength and lightweight properties. They are being increasingly utilized in the construction industry, particularly in bridge cables and building structures. However, due to their relatively poor transverse mechanical properties compared to steel cables, securing these tendons with anchors presents a challenge. This paper reviews the structure and force characteristics of three types of anchors for CFRP tendons—clamping anchorage, bonded anchorage, and composite anchorage—analyzes and summarizes the anchorage characteristics and damage mechanisms of each type of anchorage, and highlights that the optimization of the mechanical properties of the tendons is key to the design and research of anchoring systems. The new composite anchorage offers comprehensive advantages, such as minimal tendon damage at the anchorage section, more uniform stress distribution, and better anchorage performance, despite being more complex in design compared to single-type anchorages. However, there remain challenges and research gaps in testing and validating these anchoring systems under realistic loading and environmental conditions, including impacts, cyclic stresses, humidity, and high temperatures. Future efforts should focus on developing new testing techniques and models to simulate real-world conditions, enabling more accurate assessments of anchorage performance and longevity. By doing so, we can fully harness the mechanical properties of CFRP tendons and further enhance the safety and efficiency of our built environment.