Composite action between concrete and embedded reinforcement is ensured by bond developing on the interface during the hardening process of concrete. Crack formulation and size and the consequent deformation of the whole member, anchorage of reinforcing bars as well as transfer of prestress from tendons to concrete are all governed by force transfer between reinforcement and concrete that is fundamentally affected by bond. Bond is physically described and can be characterized by the local bond stress-slip (b-s) relationship influenced not only by the surface and mechanical properties of the contacting materials, time dependency of their long-term deformation and degradation due to environmental exposure but also the cyclic character of loading and many other parameters. Although several local bond stress-slip models have been elaborated for ribbed reinforcing bars by deeply investigating its influencing parameters, surprisingly low number of experimental-based data are available in the literature on the bond behaviour of steel prestressing strands and especially of group of strands irrespectively of their wide use in the prefabrication industry. From analysis point of view bond is very rarely represented in numerical models of recent time; usually full bond (i.e. no slip) on the bar-concrete interface is assumed. Similarly to that, the available analytical procedures focusing on crack- and anchorage-related parameters consider bond in a relatively simple way. The aim of the current research is the elaboration of local bond stress-slip models for prestressing strands and for group of strands as well as their application in describing bond-sensitive processes (transfer of prestress, stress distribution and splitting of prestressed beam ends, cracking) of pre-tensioned concrete members. The PhD research shall complete an extensive literature review based on which a comparative analysis of existing bond models should be carried out especially focusing on classification, limits of applicability and level of standardization. The proposed research methodology includes: (i) experimental description of local bond stress-slip law on strands and group of strands by existing standardized or appropriately improved bond tests, (ii) numerical 3D modelling of bond (development of both surface and interface models), (iii) improvement of available calculation methods for pre-tensioned members based on bond as governing effect.