Abstract: The continuous improvements in quality and cost effectiveness of second-generation high-temperature superconducting (2G-HTS) tape has greatly encouraged research institutes worldwide to develop magnets based on REBa₂Cu₃O_{7− δ} (RE123) tape. Different from low temperature superconducting wire, these RE123 tapes exhibit higher current carrying capacity and in-field performance, and hence can generate magnetic fields greater than 24 T, which cannot be achieved with the wire. However, 2G-HTS tape faces a few practical challenges, such as hysteresis and screening problems, mechanical strength, and costs, so further research and optimization of material and magnet design are required. This article first describes the 2G-HTS tape used for magnet winding, including material manufacture, in-field performance, and stress-strain effects. Second, the main issues in the fabrication of these magnets are discussed, including coil design, quench protection, screening current effects, and hysteresis losses. Finally, the recent progress of some leading research institutes are summarized, including the design, technical characteristics and operation performance of 2G-HTS magnets.