Coating thin liquid films with complex rheological behaviour on permeable substrates is often an important requirement in several applications such as contact lenses, textiles, and paper-based electronics. Here, we extend the classical Landau-Levich problem of dip coating of Newtonian liquids on rigid substrates to liquids of power-law rheology on permeable substrates. Our results suggest distinct deviation from the classical Landau-Levich relation through exhibition of different regimes of varying dependence of coating film thickness on withdrawal speed. A process map is presented depicting these coating thickness regimes for a wide range of operating parameters such as the substrate permeability factor, power-law exponent of the liquid, and a rescaled capillary number. © 2021 Elsevier Ltd