Wannier functions are often used to interpolate bandstructures calculated ab initio on a coarse grid of k -points to any arbitrary k -point. This is particularly useful for evaluation of Brillouin-zone integrals on dense grids and searching of Weyl points, and also taking derivatives in the k -space. This approach is similar in spirit to the tight binding approximation, but in contrast allows for an exact description of bands in a certain energy range. Wannier interpolation schemes have been derived for spectral properties, anomalous Hall conductivity, orbital magnetization, thermoelectric and electronic transport properties, gyrotropic effects, shift current, spin Hall conductivity and other effects.