A review of papers in the field of the line-mixing effect on IR absorption band shapes is presented, with most attention being paid to work carried out at the Molecular Spectroscopy Laboratory of St. Petersburg University. After general formulation of the problem, the empirical methods of rotational relaxation matrix evaluation are considered, and the strong collision model is discussed in more detail. The method of far band wing calculation, which takes into consideration both line mixing and the finite collision duration effect, shows the important role of line mixing in far wing shape formation. In the Markov approximation, line mixing is considered semiclassically. The classical distribution of the angular momentum alteration probability in collisions is used for reconstruction of Γ matrices which describe line broadening, line shifting and line mixing effects in the discrete rotational state representation. This method is shown to give acceptable results for the prediction of line mixing effects for central regions of Σ-Σ bands of diatomic and linear molecules.