Lyapunov exponents and Lyapunov vectors are precious tools to study dynamical systems: they provide a mathematical framework characterizing sensitive dependence on initial conditions, as well as the stretching and the contraction occurring along a trajectory. Their extension to finite size and finite time calculation has been shown to lead to the location of coherent Lagrangian Structures, which correspond in geophysical flows to frontal regions. In this case, the Lyapunov exponent and the Lyapunov vector provide respectively the cross front gradient amplification and the front orientation. Here we present global maps of Lyapunov exponents/vectors computed from satellite-derived surface currents of the oceans and we quantify their capability of predicting fronts by comparing with Sea Surface Temperature images. We find that in high energetic regions like boundary currents, large relative separations are achieved in short times (few days) and Lyapunov vector mostly align with the direction of jets; in contrast, in lower energetic regions (like the boundaries of subtropical gyres) the Lyapunov calculation allows to predict tracer lobes and filaments generated by the chaotic advection occurring here. These results may be useful for a global calibration and validation of the Lagrangian technique for multidisciplinary oceanographic applications like colocalization of marine animal behaviours to frontal systems and adaptive strategies for biogeochemical field studies.