Diffusion models, both linear and non-linear, describe important practical situations of material dynamics. Among them, the fractional diffusion equations, the classic and local ones, relevant to the anomalous diffusion, cover the broadness of their physical applications arising in heat and mass transfer through disordered media. Fractional calculus started to be utilized successfully in many areas of science and engineering. More recently, the definitions of the local fractional derivatives were presented to solve the non-differentiable problems in fractal time-space. The local version of PFD defined on Cantor sets and their solutions were developed with the help of local fractional functional techniques. This special issue titled NONLINEAR DIFFUSION MODELS IN HEAT AND MASS TRANSFER consists of 34 papers which are divided into 3 main parts.