The metal NMR parameters of the complexes [(NC)(5)Pt-Tl(CN)(n)](n -) (n = 0-3, I-IV) and [(NC)(5)Pt-Tl-Pt(CN)(5)](3-) (V), as well as [{Pt(NO(3))(NH(3))(2)L(2)}Tl(NO(3))(2)(MeOH)] (VI) and [{Pt(NO(3))(NH(3))(2)L(2)}(2)Tl](+) (VII) with L = NHCO(t)Bu, were computationally investigated by relativistic density functional theory. Complexes I-V were previously studied by us. We briefly review the main findings here. Their spin-spin coupling constants are analyzed in terms of molecular orbital and fragment orbital contributions which demonstrate the various influences of the solvent and of the ligands on the extraordinarily large metal-metal coupling constants. Complexes VI and VII and various model systems were investigated in more detail. It is shown that the same computational model which performs best for I-V yields too large metal-metal coupling constants for VI and VII. The analysis shows that this is likely to be attributable to a strong sensitivity of the coupling constants to the rather small Pt 6s contributions in the occupied metal-metal sigma-bonding orbitals. Bulk solvent effects on the metal-metal couplings are sizeable and should be considered in the computational model. Both calculated and experimental Pt--Tl coupling constants for VI and VII are substantially larger than those for I-V, thereby representing the largest heteronuclear coupling constants known so far experimentally. Metal chemical shifts for VI and VII were also investigated. The computational results indicate that the choice of the Pt reference is rather problematic. Tl chemical shifts agree much better with experimental data.