  Tight-binding models for ultracold atoms in optical lattices can be properly
defined by using the concept of maximally localized Wannier functions for
composite bands. The basic principles of this approach are reviewed here, along
with different applications to lattice potentials with two minima per unit
cell, in one and two spatial dimensions. Two independent methods for computing
the tight-binding coefficients - one ab initio, based on the maximally
localized Wannier functions, the other through analytic expressions in terms of
the energy spectrum - are considered. In the one dimensional case, where the
tight-binding coefficients can be obtained by designing a specific gauge
transformation, we consider both the case of quasi resonance between the two
lowest bands, and that between s and p orbitals. In the latter case, the role
of the Wannier functions in the derivation of an effective Dirac equation is
also reviewed. Then, we consider the case of a two dimensional honeycomb
potential, with particular emphasis on the Haldane model, its phase diagram,
and the breakdown of the Peierls substitution. Tunable honeycomb lattices,
characterized by movable Dirac points, are also considered. Finally, general
considerations for dealing with the interaction terms are presented.
