The indirect nuclear spin-spin coupling is rationalized via electronic current densities induced by nuclear magnetic dipoles. The coupling-density tensor, a function in real space obtained from the current density, visualizes fundamental aspects of the coupling mechanism. Magnetic group theory and current-density plots are used for discussing the Dirac-van Vleck vector model in the contact interaction. The Biot-Savart law is useful for understanding the sign of the contributions to the magnetic field at a nucleus from a given point of the current field. These tools are used to analyze the vicinal spin-spin coupling in ethane. (c) 2005 Elsevier B.V. All rights reserved.