  We theoretically map out the ground state phase diagram of interacting
dipolar fermions in one-dimensional lattice. Using a bosonization theory in the
weak coupling limit at half filing, we show that one can construct a rich phase
diagram by changing the angle between the lattice orientation and the
polarization direction of the dipoles. In the strong coupling limit, at a
general filing factor, we employ a variational approach and find that the
emergence of a Wigner crystal phases. The structure factor provides clear
signatures of the particle ordering in the Wigner crystal phases.
