There have been significant advances in the calculation and interpretation of indirect nuclear spin-spin coupling (J) tensors during the past few years; however, much work remains to be done, especially for molecules containing heavy atoms where relativistic effects may play an important role. Many J tensors cannot be explained based solely on a nonrelativistic Fermi-contact mechanism, In the present work, the relativistic zeroth-order regular approximation density-functional (ZORA-DFT) implementation for the calculation of J has been applied to the complete series of homonuclear and heteronuclear diatomic halogen molecules: F-2, Cl-2, Br-2, I-2, At-2, ClF, BrF, IF, ClBr, CII, and BrI. For all of these compounds, the reduced isotropic coupling constant (K-iso) is positive and the reduced anisotropic coupling constant (DeltaK) is negative. With the exception of molecular fluorine, the magnitudes of K-iso and DeltaK are shown to increase linearly with the product of the atomic numbers of the coupled nuclei, ZORA-DFT calculations of J for F-2 and ClF are in excellent agreement with the results obtained from multiconfigurational self-consistent-fie Id calculations, The relative importance of the various coupling mechanisms is approximately constant for all of the compounds, with the paramagnetic spin-orbit term being the dominant contributor to K-iso, at approximately 70-80%. Available experimental stimulated resonant Raman spectroscopy data are exploited to extract the complete J(I-127,I-127) tensor for iodine in two rotational states, The dependence of K-iso and DeltaK on bond length and rovibrational state is investigated by using calculated results in combination with available experimental data. In addition to providing new insights into periodic trends for J coupling tensors, this work further demonstrates the utility of the ZORA-DFT method and emphasizes the necessity of spin-orbit relativistic corrections for J calculations involving heavy nuclei.