A large body of evidence, including the presence of a dynamical family associated with 4 Vesta, suggests that this asteroid might be the ultimate source of both the V-type Near-Earth asteroids (NEAs) and HED meteorites. Dynamical routes from Vesta to the inner regions of the Solar System are provided by both the 3:1 mean-motion resonance with Jupiter and the v6 secular resonance. For this reason, numerical integrations of the orbits of fictitious Vesta fragments injected in both of these resonances have been performed. At the same time, the orbital evolution of the known V-type NEAs has been investigated. The results indicate that the dynamical half lifetimes of Vesta fragments injected in both the 3:1 and the v6 resonances are rather short (<2 Myr). The most important result is that the present location of the 7 known V-type NEAs is well explained by orbital evolution of ejecta starting from the v6 secular resonance. However, we now face what we call the ``Vesta paradox''. Roughly speaking, the paradox consists of the fact that the present V-type NEAs appear to be too dynamically young to have originated in the event that produced the family, but they are too big to be plausible second-generation fragments from the family members. The CRE age distribution of HED meteorites also raises a puzzle, since we would expect an overabundance of meteorites with short CRE ages. We propose different scenarios to explain these paradoxes.