The basic structure of the Varroa mite and honey bee relationship is described to allow the construction of a mathematical model of the mite population dynamics. Necessary criteria for building the model is commented. In the mite reproduction part of the model, the demand of relevant bee brood data and the understanding of variations in mite fertility, especially on worker brood, are emphasised. In the mite mortality part of the model, it is pointed out that there is a lack of information on the proportion of mites that die but that do not end up in the hive debris. In cold climates, the loss of mites, as bees die during winter is important to limit the mite population growth. In regions with extended brood rearing, mite mortality data during flying conditions is vital. The presented model does not include the effect of mites on bee population dynamics. Thus, it is only relevant for infestation levels below a certain threshold. Such a model may still be used for simulating effects of control treatments or breeding programmes for mite tolerance. Simulations indicate that the proportion of infertile mites in the worker brood is a key factor for limiting mite population growth.