This Ph.D. thesis is focused on the development of novel models for calculation of AC losses, current and magnetic field profiles in high-temperature superconductors (HTS). The thesis is concentrated on the modelling of Bi-2223 conductors at 77 K, which for the moment have the most advanced manufacturing technology and will be primarily used in the first large-scale power applications of high-temperature superconductors. The analysis of AC losses in Bi-2223 conductors is the leading thread in the structure of the thesis. An introduction to high-temperature superconductivity is made with special emphasis on the mechanisms of AC losses in HTS. Presented are some of the most promising power applications of HTS materials together with a discussion on the required improvements in their performance. A model for dissociating the hysteresis, eddy-current and resistive flux-creep loss contributions, based on relatively broad-range frequency measurements on Bi-2223 tapes has been used for analysis of the frequency behaviour of the transport-current loss in self-field. The hysteresis, eddy-current and flux-creep loss components have been separated due to their different frequency dependence. The study of eddy current loss in the silver sheath and matrix has been complimented by numerical simulations using a simple electromagnetic model of HTS tapes. Described is an original method for estimating the performance of Bi-2223 tapes in typical power grid perturbations by experiments and analysis of over-critical current excursions of various waveform, frequency and current amplitude up to 20×Ic. For precise calculation of the AC losses and studying the electromagnetic properties of HTS with smooth current-voltage characteristics and complex geometry, the finite element method (FEM) has been used. The implementation of the power-law model of the E-J characteristic of HTS into the FEM software package Flux2D is presented. The Flux2D implementation has been validated by means of comparison with results from theoretical predictions, electrical measurements, and other numerical methods. The significance of the power index n and the lateral distribution of the critical current density Jc in multifilamentary HTS tapes has been evaluated by FEM simulations. New anisotropic models of Jc(B) and n(B) for textured Bi-2223 materials have been developed. The models are based on experimental data; they are fairly simple and take into account the orientation of the local magnetic field. These models have been used in FEM simulations on monofilamentary and multifilamentary Bi-2223 conductors with different geometry and filament arrangement. In conductors with given Jc(B) dependence, the notion of effective AC critical current has been defined. The AC losses in Bi-2223 multifilamentary flat tapes and wires of round and square geometry in various operating conditions have been calculated and compared. The AC loss analysis has been supported and complimented by current density and magnetic flux distributions in the different conductors. The influence of the shape factor of the geometry and the filament orientation with respect to the local magnetic field has been thoroughly investigated. The optimal geometry and filament arrangement have been determined for each application.