  We show that backflow correlations in the variational wave function for the
Hubbard model greatly improve the previous results given by the Slater-Jastrow
state, usually considered in this context. We provide evidence that, within
this approach, it is possible to have a satisfactory connection with the
strong-coupling regime. Moreover, we show that, for the Hubbard model on the
lattice, backflow correlations are essentially short range, inducing an
effective attraction between empty (holons) and doubly occupied sites
(doublons). In presence of frustration, we report the evidence that the metal
to Mott-insulator transition is marked by a discontinuity of the double
occupancy, together with a similar discontinuity of the kinetic term that does
not change the number of holons and doublons, while the other kinetic terms are
continuous across the transition. Finally, we show the estimation of the charge
gap, obtained by particle-hole excitations {\it \`a la Feynman} over the
ground-state wave function.
