Since the discovery of high temperature superconductors (HTS) more than 2 decades ago, there has been interest in their use for future fusion machines. Lack of performance of commercially available materials, however, dampened the initial optimism. However, recent advances in HTS materials, mostly second-generation tapes, open attractive topologies. In addition to reduced cryogenic loads and increased superconducting stability, the HTS tapes may allow demountable magnets that could be very helpful in the long term (for reactor maintenance) and in the intermediate term, for component-testing machines which require large access. Tests on joints have demonstrated that the thermal load due to the Joule dissipation in these joints is small, allowing operation with very long pulses without restrictions on cost of electricity or power availability. There are challenges in the use of HTS in magnets in general, and fusion specifically. The excellent properties of HTS materials, e.g., YBCO (YBa2Cu3O7-δ) superconductors operating at elevated temperatures (> 30K) also offer operational advantages for fusion machines, but there are challenges, such as the manufacturing of high current cables and methods of quench protection. In addition to tapes, HTS can be fabricated as monoliths. These monoliths offer the possibility of field control for complex geometries, such as generating stellarator-like fields from simple toroidal fields. This paper summarizes work at MIT and in Japan on concept development and testing, as well as challenges ahead.