Methods for the calculation of atom-molecule dispersion coefficients are reviewed, with emphasis on approximate techniques. New results are reported for the interaction of several S-state atoms with ground-state molecular hydrogen using the Padé bounding technique. The scarcity of data for the dependence on the intramolecular coordinate imposes the use of approximate schemes to interpolate and extrapolate the dispersion coefficient for regions where it is unknown. Several approaches are suggested based on the Unsöld approximation and the Kirkwood variational method.