Kozai-Lidov mechanism is a major source of dynamical evolution in multiple stellar systems and in young planetary systems with large mutual inclinations. It drives orbital eccentricities to very high values while keeping semi-major axes constant, thus reducing periastron distances. Furthermore, tidal friction at periastron acts at shrinking orbits and generating misaligned close-in planets and tight pairs in triple stellar systems. GJ 436b is a short period transiting Neptune-mass exoplanet orbiting an M dwarf on a surprisingly eccentric orbit. Tides should have already circularized its orbit. In an earlier study (Beust et al. 2012, A&A 545, A88), we showed that Kozai migration combined with tides could have delayed the circularization of this planet and explain the residual eccentricity. This model implies the presence of another yet unknown body at larger distance in this system. It also predicts that GJ 436b's orbital plane should be tilted with respect to the stellar equator. We report here the recent detection of this spin-orbit misalignment, derived by mapping the spectrum of the stellar protosphere along the chord transited by the planet. GJ 436b orbits nearly perpendicularly to the stellar equator (Bourrier et al. 2018, Nature 553, 477). This result reinforces the 2012 hypothesis, and allows us to derive additional constraints on the dynamical model, in particular concerning the mass and the distance of the hypothetical perturber. The inward migration of GJ 436b could have triggered the atmospheric escape that now sustains its giant exosphere.