The Method of Dimensionality Reduction (MDR) can be regarded as a formalism for analytical solution of some commonly encountered classes of contact problems using a "mechanical intuition" based on the Winkler foundation model. Such an approach makes it much easier to account for a wide range of physical effects associated with contact interaction (e.g. friction, adhesion, and damping). However, there is still a controversy about the method and its applications (see, e.g., the comment on validity of the MDR-based model of rough contact) – which we believe comes from a misunderstanding of the method itself, and which, in turn, can be reconsidered in view of the recently published book on the MDR. The MDR was originally introduced for Hertz’s problem of axisymmetric frictionless local contact and was generalized subsequently for arbitrary axisymmetric geometry of linearly elastic bodies in unilateral local contact. The latter problem, for which the MDR yields the exact analytical solution, can be viewed as a base case that is used to extend, in a unified manner, the model of local contact by taking into account adhesion, friction, and viscous damping. In what follows, we overview the main concepts of the method starting with the base-case contact problem in which the MDR is rooted, and discuss limitations of the MDR as well. For the sake of their completeness, some criticisms that apply equally to conventional contact mechanics solutions are also considered. It is emphasized that the axisymmetric Hertz-type contact problems with a circular contact area constitute the proven range of validity of the MDR, while the extension of the method to other types of contact (e.g. axisymmetric with a multiply-connected contact area, non-axisymmetric) is a field ripe for research.