In the authors' words, ``the mathematical approach to general relativity insists that all coordinate systems are equal''. In contradiction to this ``doctrine'' the authors claim that, for some problems in general relativity, restriction to a subclass of coordinates is not only convenient to simplify calculations but even necessary to understand the physics of the situation at hand. This claim is illustrated by the Newtonian limit of general relativity, by the gauge issue in cosmology, and by certain aspects of numerical relativity. The paper is non-technical in the sense that it contains not a single formula.