Particle colliders are the main tool for investigating and understanding the fundamental laws of physics. The CERN Large Hadron Collider (LHC), is a circular accelerator which steers and collides two counter-rotating protons beams. It has four collision points where detectors are placed to analyze the products emerging from the collisions. In a synchrotron machine a magnetic flux density is used to guide and focus particles around the orbit. The maximum energy that a circular machine with a given geometry can achieve is limited by the maximum strength of the dipole magnetic flux density. There is therefore an interest in the particle physics community in searching for dipole magnets with higher strength. The LHC has a beam trajectory radius of 4.3 km and a collision center-of-mass energy of 14 TeV. The accelerator employs 1232 large superconducting Nb-Ti dipole magnets operated at a flux density of up to 8.3 T in a bath of superfluid helium at 1.9 K. Energies higher than that achieved with the LHC require magnets made from superconductors with higher upper critical flux density. Nb3Sn is an option for magnets operated up to about 14 T. The level of energies of the type being discussed for a potential energy upgrade of the LHC machine - 33 TeV- would require the use of high temperature superconductors (HTS). Three technical HTS are available today: YBCO, Bi-2212 and Bi-2223. At low temperature YBCO conductors present both irreversible flux density and current density in excess of those measured in Bi-2212 and Bi-2223 conductors. In addition, YBCO can be used as reacted conductor, which makes its use for applications simpler than Bi-2212, which requires heat treatment at high temperature and in oxygen atmosphere after cabling and winding. The level of currents required for application to accelerator magnets, which is above 10 kA at the nominal operating temperature and flux density, excludes the use of single strands. The high current and high current density required can be achieved with cables having several strands connected in parallel. The main objective of my work has been the study of HTS cables for high current/high current density applications, starting from the analysis and selection of suitable conductors, through the characterization of their intrinsic (e.g. critical surface, strain sensitivity and irreversible strain) and extrinsic (e.g. cabling degradation) properties, with the final objective of validating 10 kA-range cables based on HTS material for high flux density magnets. The performance of YBCO and Bi-2223 tapes at 4 K under parallel and perpendicular flux density is measured using purpose built samples holders. A complete review of the strain sensitivity of HTS materials is presented, and the measured critical current retention of HTS tapes under torsion is discussed. Expressions that describe the critical current density of HTS conductors as a function of flux density strength, flux density orientation, temperature and strain are introduced. Analytical models that provide the allowable twist and bending radius of YBCO tapes as a function of strain are elaborated and compared with measurements. The accurate expressions are then used to compute the margins of the winding pack of a 19 T dipole made with a YBCO cable. Roebel cables made of YBCO high current strands are characterized at 4.2 K and in flux densities of up to 9.6 These are the first measurements ever performed at 4.2 K and with high currents. The Roebel cables reached critical currents of up to 12 kA with engineering current density in excess of 1.1 kA/mm2 at 7.5 T. These measurements demonstrate the potential of Roebel cables for high flux density magnets. During measurements two out of four Roebel cables were irreversibly damaged. The mechanism of failures is detailed and explained. Finally the performance and current distribution of HTS cables is computed and compared with measurements