High temperature superconducting (HTS) materials have the potential to generate a magnetic field beyond the level obtainable with low temperature superconducting (LTS) materials. This review reports on past and present R&D on HTS cables and conductors for high field tokamaks, accelerator dipoles, and large solenoids. Among the HTS wires and tapes available commercially, coated conductor tapes are the most appealing because of their outstanding critical strength and future improvement margin. Limitations are the weakness against peeling and delamination and the short piece length. The prices of technical superconductors are reviewed because they play an important role in large projects; moreover HTS wires and tapes are discussed from the perspective of industrial production considering the historical development of the LTS wire market. Various designs have been proposed for HTS cables and conductors: some are better suited for soft materials, while others can exploit the anisotropy of coated conductors (by aligning the tape with the field), thus providing the highest current density. Recently, there has been an increase in the size and complexity of the prototypes; however some peculiar features of HTS, such as high stability margins and high mechanical limits, have not yet been fully incorporated into the designs: for example the transposition requirements for HTS have not yet been studied in detail. There are elements indicating that rectangular wires and tapes (even if anisotropic) can be used for manufacturing cables and magnets of any size and have advantages with respect to round wires.