High Temperature Superconducting (HTS) materials have the potential to generate magnetic field beyond the level obtainable with Low Temperature Superconducting (LTS). This review reports the 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 the outstanding critical strength and large improvement margin. Limitations are the weakness against peeling and shearing and the short piece length. The prices for technical superconductors are reviewed because they play an important role in large projects; moreover the perspective of industrial production of HTS wires and tapes is discussed 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), providing the highest current density. The last decade has seen an increase in the size and complexity of the prototypes; however some peculiar features of HTS, such as high stability margin and high mechanical limits, have not yet been fully incorporated in the designs: for example the transposition requirements for HTS have not yet been studied in detail. Several facts indicate that tapes (even if anisotropic) can be used for manufacturing cables and magnets of any size and have advantages with respect to round wires.