Ability to migrate is a fundamental property of all animal cells. Cell migration underlies such important physiological and pathological processes as embryonic development, immune response, tissue regeneration and cancer metastasis. As cell migration involves forces and motion, it is ultimately a physical phenomenon that should be understood in terms of fundamental physical laws. Cell migration mechanisms are based on the activity of the cytoskeleton, a system of intracellular filaments and motor proteins. During cell migration, forces developed by the cytoskeleton are transmitted, through specific adhesions complexes, to the substrate. Composition and dynamics of the cytoskeleton has been subject of many studies, but it remains poorly understood how the cytoskeleton reactions and its interaction with extra cellular matrix are orchestrated to result in coordinated migration behavior. The main part of this thesis consists of the experiments and analysis of force transmission during cell migration in the experimental system of fish epidermal keratocytes. Our experimental approaches involved microinjection for proteins dynamics quantification, micromanipulation, use of compliant substrate, simultaneous imaging of cytoskeleton and substrate deformation, and the use of cytoskeletal inhibitors. In parallel with the experiments, significant computational work has been performed to program and adapt existing algorithms to analyze experimental data. Thanks to the combination of our experimental and computational approaches, we were able to correlate actin dynamics and traction forces over the whole cell, to map the efficiency of force transmission, and to reveal slipping and gripping mechanisms differentially involved in stress transmission in different parts of the cell. We also investigated contributions of actin assembly and myosin-dependent contractility to force generation and provided evidence that cell translocation could be powered by two different engines. Additionally, we performed micromanipulation experiments to identify the cell polarity cues associated with specific cytoskelatal reactions and regions of the cell. We have also collaborated with the laboratory of one of the leading modellers in the field of cell biophysics to validate a new mathematical model of cell migration and force transmission.